Application of 1st Order Differential Equation
Laws of growth and decay/decomposition of growth/Radioactive decay
![Application of 1st Order Differential Equation & Examples 1 Laws of growth and decay/decomposition of growth/Radioactive decay](https://theskyscorner.com/wp-content/uploads/2023/03/image-18.png)
Population 60 000 in 1990, increased to 63 000 by 2000. Estimate the population in 2010.
![Application of 1st Order Differential Equation & Examples 2 Laws of growth and decay/decomposition of growth/Radioactive decay. Population 60 000 in 1990, increased to 63 000 by 2000. Estimate the population in 2010.](https://theskyscorner.com/wp-content/uploads/2023/03/image-19.png)
Logistic Growth Equation and Analytic Solution
![Application of 1st Order Differential Equation & Examples 3 Logistic Growth Equation and Analytic Solution](https://theskyscorner.com/wp-content/uploads/2023/03/image-20.png)
Use the exact solution to determine when the population will reach 450. Po = 500. Logistic growth?
![Application of 1st Order Differential Equation & Examples 4 Use the exact solution to determine when the population will reach 450. Po = 500. Logistic growth?](https://theskyscorner.com/wp-content/uploads/2023/03/image-22.png)
![Application of 1st Order Differential Equation & Examples 5 Use the exact solution to determine when the population will reach 450. Po = 500. Logistic growth?](https://theskyscorner.com/wp-content/uploads/2023/03/image-23.png)
Logistic Equation and Models For Population
Differential equation solve. Logistic Equation and Models For Population.
Biologist stock a lane with 500 fish and estiamte the carrying capacity to be 10,000. The number of fish tripled during the first year.
Assuming that the size of the fish population satisfies the logistic equation, find an expression for the size of the population after w years.
![Application of 1st Order Differential Equation & Examples 6 Differential equation solve. Logistic Equation and Models For Population.
Biologist stock a lane with 500 fish and estiamte the carrying capacity to be 10,000. The number of fish tripled during the first year.
Assuming that the size of the fish population satisfies the logistic equation, find an expression for the size of the population after w years.](https://theskyscorner.com/wp-content/uploads/2023/03/image-24.png)
![Application of 1st Order Differential Equation & Examples 7 Differential equation solve. Logistic Equation and Models For Population.
Biologist stock a lane with 500 fish and estiamte the carrying capacity to be 10,000. The number of fish tripled during the first year.
Assuming that the size of the fish population satisfies the logistic equation, find an expression for the size of the population after w years.](https://theskyscorner.com/wp-content/uploads/2023/03/image-25.png)
![Application of 1st Order Differential Equation & Examples 8 Differential equation solve. Logistic Equation and Models For Population.
Biologist stock a lane with 500 fish and estiamte the carrying capacity to be 10,000. The number of fish tripled during the first year.
Assuming that the size of the fish population satisfies the logistic equation, find an expression for the size of the population after w years.](https://theskyscorner.com/wp-content/uploads/2023/03/image-26.png)
Population Growth: Exponential
![Application of 1st Order Differential Equation & Examples 9 Population Growth: Exponential](https://theskyscorner.com/wp-content/uploads/2023/03/image-27.png)
Population Growth: Exponential/
A population that starts with 500 people, increases by 15% in 10 years. What is the population in 30 years?
![Application of 1st Order Differential Equation & Examples 10 Population Growth: Exponential/
A population that starts with 500 people, increases by 15% in 10 years. What is the population in 30 years?](https://theskyscorner.com/wp-content/uploads/2023/03/image-28.png)
![Application of 1st Order Differential Equation & Examples 11 It is known that the population of a certain country at time t is proportional to the people living in it presently. If after 2 years, the population is tripled the original, find the number of people intially.](https://theskyscorner.com/wp-content/uploads/2023/03/image-29.png)
It is known that the population of a certain country at time t is proportional to the people living in it presently. If after 2 years, the population is tripled the original, find the number of people initially.
![Application of 1st Order Differential Equation & Examples 12 It is known that the population of a certain country at time t is proportional to the people living in it presently. If after 2 years, the population is tripled the original, find the number of people intially.](https://theskyscorner.com/wp-content/uploads/2023/03/image-30.png)
https://googleads.g.doubleclick.net/pagead/ads?client=ca-pub-4992295247869184&output=html&h=280&slotname=3523241294&adk=1745771614&adf=3408513213&pi=t.ma~as.3523241294&w=1140&fwrn=4&fwrnh=100&lmt=1678887284&rafmt=1&format=1140×280&url=https%3A%2F%2Ftheskyscorner.com%2Fapplication-of-1st-order-differential-equation-2%2F&host=ca-host-pub-2644536267352236&fwr=0&fwrattr=true&rpe=1&resp_fmts=3&wgl=1&adsid=ChEI8NnFoAYQmbznopqLlqmFARI5APsQfT7qNVKC6dPJZaBpXGIs9aMmM0L5UHzMmBuONKoP5JKQ0vG8mjLAa7NMiieL-_5qxooprtE2&uach=WyJXaW5kb3dzIiwiMTAuMC4wIiwieDg2IiwiIiwiMTExLjAuNTU2My42NSIsW10sZmFsc2UsbnVsbCwiNjQiLFtbIkdvb2dsZSBDaHJvbWUiLCIxMTEuMC41NTYzLjY1Il0sWyJOb3QoQTpCcmFuZCIsIjguMC4wLjAiXSxbIkNocm9taXVtIiwiMTExLjAuNTU2My42NSJdXSxmYWxzZV0.&dt=1678887279058&bpp=4&bdt=826&idt=168&shv=r20230313&mjsv=m202303070101&ptt=9&saldr=aa&abxe=1&cookie=ID%3D6cd1f1ff6279f1cc-2242116981d1006a%3AT%3D1648817502%3ART%3D1648817502%3AS%3DALNI_Ma9X2EQPzgi9Yop6bNYKYchVVZSQg&gpic=UID%3D000007e1014b904d%3AT%3D1658289413%3ART%3D1678882871%3AS%3DALNI_MbfQlk3wHmEW6CqU9kfpAzoAYs2aw&prev_fmts=1140×280&correlator=3861810458241&frm=20&pv=1&ga_vid=168115324.1648817501&ga_sid=1678887279&ga_hid=1786186301&ga_fc=1&u_tz=480&u_his=1&u_h=864&u_w=1536&u_ah=824&u_aw=1536&u_cd=24&u_sd=1&dmc=8&adx=380&ady=7449&biw=1899&bih=902&scr_x=0&scr_y=3848&eid=44759837%2C44777877%2C44759876%2C44759927%2C31072915%2C31072951%2C44774606%2C44786424%2C31071976%2C31072922&oid=2&pvsid=2836572455616639&tmod=1041978388&uas=3&nvt=1&ref=https%3A%2F%2Ftheskyscorner.com%2Fwp-admin%2Fedit.php%3Fpost_status%3Dpublish%26post_type%3Dpage%26orderby%3Ddate%26order%3Ddesc&fc=1920&brdim=0%2C0%2C0%2C0%2C1536%2C0%2C1536%2C824%2C1920%2C902&vis=1&rsz=%7C%7CoeEbr%7C&abl=CS&pfx=0&fu=128&bc=31&jar=2023-03-10-01&ifi=3&uci=a!3&btvi=2&fsb=1&xpc=34qYhU3vQ8&p=https%3A//theskyscorner.com&dtd=5099
Laws of Growth and Decay
![Application of 1st Order Differential Equation & Examples 13 Differential equation. Laws of growth and decay.](https://theskyscorner.com/wp-content/uploads/2023/03/image-31.png)
Differential equation. Laws of growth and decay.
Radium decomposes at the air at the rate proportional to the present amount. If initially there are 20 grams, and after 10 years, 06% of the original amount decomposed.
A. Set a model that will predict the amount of radium at any time t.
![Application of 1st Order Differential Equation & Examples 14 Differential equation. Laws of growth and decay.
Radium decomposes at the air at the rate proportional to the present amount. If initially there are 20 grams, and after 10 years, 06% of the original amount decomposed.
A. Set a model that will predict the amount of radium at any time t.](https://theskyscorner.com/wp-content/uploads/2023/03/image-32.png)
What is the half life of the radium?
![Application of 1st Order Differential Equation & Examples 15 Differential equation. Laws of growth and decay.
Radium decomposes at the air at the rate proportional to the present amount. If initially there are 20 grams, and after 10 years, 06% of the original amount decomposed.
A. Set a model that will predict the amount of radium at any time t. What is the half life of the radium?](https://theskyscorner.com/wp-content/uploads/2023/03/image-33.png)
![Application of 1st Order Differential Equation & Examples 16 Application of 1st Order Differential Equation & Examples image 34](https://theskyscorner.com/wp-content/uploads/2023/03/image-34.png)
![Application of 1st Order Differential Equation & Examples 17 Application of 1st Order Differential Equation & Examples image 35](https://theskyscorner.com/wp-content/uploads/2023/03/image-35.png)
![Application of 1st Order Differential Equation & Examples 18 Application of 1st Order Differential Equation & Examples image 36](https://theskyscorner.com/wp-content/uploads/2023/03/image-36.png)
Radium decomposes at a rate proportional to the amount present. If the half life is 1600 years, find the percentage remaining at the end of 200 years.
![Application of 1st Order Differential Equation & Examples 19 Radium decomposes at a rate proportional to the amount present. If the half life is 1600 years, find the percentage remaining at the end of 200 years.](https://theskyscorner.com/wp-content/uploads/2023/03/image-37.png)
![Application of 1st Order Differential Equation & Examples 20 Radium decomposes at a rate proportional to the amount present. If the half life is 1600 years, find the percentage remaining at the end of 200 years.](https://theskyscorner.com/wp-content/uploads/2023/03/image-38.png)
Continuous Compound Interest
![Application of 1st Order Differential Equation & Examples 21 Compound interest and differential equation.](https://theskyscorner.com/wp-content/uploads/2023/03/image-39.png)
Compound interest and differential equation.
If the nominal interest rate is 3%, how much is 5000 pesos worth in 10 years in a continuously compounded account?
![Application of 1st Order Differential Equation & Examples 22 If the nominal interest rate is 3%, how much is 5000 pesos worth in 10 years in a continuously compounded account?](https://theskyscorner.com/wp-content/uploads/2023/03/image-40.png)
![Application of 1st Order Differential Equation & Examples 23 If the nominal interest rate is 3%, how much is 5000 pesos worth in 10 years in a continuously compounded account? The accumulated amount of 5000 pesos is 20 000 pesos after 9 years. Calculate the interest rate if it is compounded continuously.](https://theskyscorner.com/wp-content/uploads/2023/03/image-41.png)
How long will it take a bank deposit to double if interest is compounded continuously at a constant rate of 4% per annum?
![Application of 1st Order Differential Equation & Examples 24 How long will it take a bank deposit to double if interest is compounded continuously at a constant rate of 4% per annum?](https://theskyscorner.com/wp-content/uploads/2023/03/image-42.png)
A depositor places 10 000 dollars in a certificate of deposit account which pays 7% interest per annum compounded continuously. How much will be in the account after two years.
![Application of 1st Order Differential Equation & Examples 25 A depositor places 10 000 dollars in a certificate of deposit account which pays 7% interest per annum compounded continuously. How much will be in the account after two years.](https://theskyscorner.com/wp-content/uploads/2023/03/image-43.png)
Newton’s Law of Cooling
![Application of 1st Order Differential Equation & Examples 26 Newtons law of cooling with differential equation](https://theskyscorner.com/wp-content/uploads/2023/03/image-44.png)
![Application of 1st Order Differential Equation & Examples 27 Application of 1st Order Differential Equation & Examples image 45](https://theskyscorner.com/wp-content/uploads/2023/03/image-45.png)
![Application of 1st Order Differential Equation & Examples 28 Application of 1st Order Differential Equation & Examples image 46](https://theskyscorner.com/wp-content/uploads/2023/03/image-46.png)
A thermometer reading 10 Celsius is brought in a room whose temperature is 18 C. One minute later, the thermometer reading is 14 C. How long does it takes until the reading becomes 16 C?
![Application of 1st Order Differential Equation & Examples 29 A thermometer reading 10 Celsius is brought in a room whose temperature is 18 C. One minute later, the thermometer reading is 14 C. How long does it takes until the reading becomes 16 C?](https://theskyscorner.com/wp-content/uploads/2023/03/image-47.png)
![Application of 1st Order Differential Equation & Examples 30 A thermometer reading 10 Celsius is brought in a room whose temperature is 18 C. One minute later, the thermometer reading is 14 C. How long does it takes until the reading becomes 16 C?](https://theskyscorner.com/wp-content/uploads/2023/03/image-48.png)
A metal is heated up to a temperature of 500 Celsius. It is then exposed to a temperature of 38 C. After 2 minutes, the temperature is 190 C. What is the time required to be in 100 C?
![Application of 1st Order Differential Equation & Examples 31 A metal is heated up to a temperature of 500 Celsius. It is then exposed to a temperature of 38 C. After 2 minutes, the temperature is 190 C. What is the time required to be in 100 C?](https://theskyscorner.com/wp-content/uploads/2023/03/image-49.png)
![Application of 1st Order Differential Equation & Examples 32 A metal is heated up to a temperature of 500 Celsius. It is then exposed to a temperature of 38 C. After 2 minutes, the temperature is 190 C. What is the time required to be in 100 C?](https://theskyscorner.com/wp-content/uploads/2023/03/image-50.png)
![Application of 1st Order Differential Equation & Examples 33 A metal is heated up to a temperature of 500 Celsius. It is then exposed to a temperature of 38 C. After 2 minutes, the temperature is 190 C. What is the time required to be in 100 C?](https://theskyscorner.com/wp-content/uploads/2023/03/image-51.png)
![Application of 1st Order Differential Equation & Examples 34 A metal is heated up to a temperature of 500 Celsius. It is then exposed to a temperature of 38 C. After 2 minutes, the temperature is 190 C. What is the time required to be in 100 C?](https://theskyscorner.com/wp-content/uploads/2023/03/image-52.png)
![Application of 1st Order Differential Equation & Examples 35 Application of 1st Order Differential Equation & Examples image 53](https://theskyscorner.com/wp-content/uploads/2023/03/image-53.png)
![Application of 1st Order Differential Equation & Examples 36 Mixing problems with differential equation](https://theskyscorner.com/wp-content/uploads/2023/03/image-54.png)
![Application of 1st Order Differential Equation & Examples 37 Mixing problems with differential equation](https://theskyscorner.com/wp-content/uploads/2023/03/image-55.png)
![Application of 1st Order Differential Equation & Examples 38 Mixing problems with differential equation](https://theskyscorner.com/wp-content/uploads/2023/03/image-56.png)
A tank contains 1 500 L of water and 20 kg of dissolved salt. Fresh water is entering the tank at 15 L/min, and the solution drains at a rate of 10 L/min. How much salt is in the tank at t minutes and at 10 minutes.
![Application of 1st Order Differential Equation & Examples 39 A tank contains 1 500 L of water and 20 kg of dissolved salt. Fresh water is entering the tank at 15 L/min, and the solution drains at a rate of 10 L/min. How much salt is in the tank at t minutes and at 10 minutes.](https://theskyscorner.com/wp-content/uploads/2023/03/image-57.png)
![Application of 1st Order Differential Equation & Examples 40 A tank contains 1 500 L of water and 20 kg of dissolved salt. Fresh water is entering the tank at 15 L/min, and the solution drains at a rate of 10 L/min. How much salt is in the tank at t minutes and at 10 minutes.](https://theskyscorner.com/wp-content/uploads/2023/03/image-58.png)
Electrical Circuit
![Application of 1st Order Differential Equation & Examples 41 Electrical circuit in differential equation](https://theskyscorner.com/wp-content/uploads/2023/03/image-59.png)
![Application of 1st Order Differential Equation & Examples 42 Electrical circuit in differential equation. An RL Circuit.](https://theskyscorner.com/wp-content/uploads/2023/03/image-60.png)
![Application of 1st Order Differential Equation & Examples 43 Electrical circuit in differential equation. An RL Circuit.](https://theskyscorner.com/wp-content/uploads/2023/03/image-61.png)
![Application of 1st Order Differential Equation & Examples 44 Application of 1st Order Differential Equation & Examples image 62](https://theskyscorner.com/wp-content/uploads/2023/03/image-62.png)
![Application of 1st Order Differential Equation & Examples 45 Electrical circuit in differential equation. An RL Circuit.](https://theskyscorner.com/wp-content/uploads/2023/03/image-63.png)