Suppose that the rate of growth of a population of organisms is proportional to the number present, t in days. if there are 10,000 individuals present in 10 days and 15,000 individuals present in 15 days when will the initial population have doubled?

My question is, is the answer as obvious as I think it is am I on the wrong track? (my guess is that in 20 days the population will be 20,000)

Question

Suppose that the rate of growth of a population of organisms is proportional to the number present, t in days. if there are 10,000 individuals present in 10 days and 15,000 individuals present in 15 days when will the initial population have doubled?

My question is, is the answer as obvious as I think it  is am I on the wrong track? (my guess is that in 20 days the population will be 20,000)

saifoo.khan · Answer

$$\Large N_t = N_0^{λt}$$

saifoo.khan · Answer

Find the value of λ, which is a constant then solve it.

anonymous · Answer

so to solve for λ would the equation be 
15,000 = 10,000 ^(λ*10) I'm a little confused

saifoo.khan · Answer

Nope. We don't know N0 either.
N0 is the initial value.

We have to make two equations.

anonymous · Answer

@saifoo.khan has the patience!

saifoo.khan · Answer

$$\Large 10000=N_0^{λ10}$$and $$\Large 15000=N_0^{15λ}$$
Now find N0 and λ.

saifoo.khan · Answer

haha @Rohangrr

anonymous · Answer

you got that right

anonymous · Answer

the equation I'm used to using for exponential growth is Pe^rt would I get the same results if I used that one?

saifoo.khan · Answer

Umm. Ops. You're right i missed e!! :/
Sorry.

Add e over there.

anonymous · Answer

thanks!

phi · Answer

fyi, you should get a number between 8 and 9 days

anonymous · Answer

yep, I did, thank you!