Algebra help homework needed

Question

A population of frogs in a nature preserve grows according to the continuous growth model P=F(T)=2200e^0.086t where P is the number of frogs and t is in years find f(0)= _____. To the nearest whole number ,find the number of frogs after 3 years ____, To the nearest tenth of a year, determine how long it will take for the population to grow to 4600 frogs ___ years.

Answer 1

Hi Angeles!

For the first question, f(0) basically means that we have to plug in 0 for t (years) and see what our output is. F(0) = 2,200e^(0.086 *0) = 2,200e ^ 0 = 2,200 frogs!

After 3 years, we would do the same thing but just plug in 3 for t. We would get 2,200e^(0.086 * 3) = 2,848 frogs.

In order to find out how many years we would take to get 4,600 frogs we would put the equation 2,200e ^ (0.086 * t) = 4,600. Dividing both sides by 2,200 we get: e ^ (0.086 * t) = 2.0909. We now have to take the natural log of both sides and we get: 0.086 * t = ln (2.0909). We use natural log to get rid of that e. We then divide both sides by 0.086 and we get an answer for t to be 8.57, or 8.6 years.

Hopefully this helps, please let me know if you have any other questions!