Question

Need help on 2 exponential growth problems please :)

Answer 1

The population of rabbits in a forest follows the law of exponential growth. There are 150 rabbits
present initially and there are 300 after 3 years.
(a) Write a function that represents the number of rabbits after t years.
(b) How many rabbits will there be in 10 years?

How do I get the function?

Answer 2

\[y=a(1+r)^{x}\]

Answer 3

start with the idea that your equation is in the form

\(N = N_o e^{kt}\)

Answer 4

That's your exponential growth equation. a is the initial amount, r is the growth rate, and x is the number of time intervals that has passed

Answer 5

Okay, I remember that equation from the lesson @IrishBoy123 , if I remember right, with the information given, it would become 300 = 150\(e^{3k}\)?

Answer 6

Then I need to get \(e^{3k}\) on the right by itself?

Answer 7

yes, just put t = 0 and t = 3 in with your other conditions and solve them

so, for t = 0 you have \(150 = N_o e^{0} = N_o\)

for t = 3 you have \(300 = 150 e^{3k}\). solve that using natural logs

but @Aveline 's idea looks good.

Answer 8

Just to make sure I remember how to solve with natural logs, I would take ln of both sides, ln 2 = 3k ln e, ln e cancels out leaving ln 2 = 3k?

Answer 9

or
\(\dfrac{300}{150} = e^{3k}\)
\(\ln \dfrac{300}{150} = 3k\)

same as you

Answer 10

Okay, thank you! :)

Answer 11

I think I can do the second problem on my own now :)