Exponential growth formula: (1+r)^t or e^(r*t)?

A population of 745 quail increases at 16% per year.
Write an exponential function for the quail population and
what is the population be after 4 years?
I answered this question yesterday and said the answer was 745*e^(r*t) = 745*2.718281828^(.16*4) =
1,412.878
However, couldn't it also be solved by
745*(1+r)^t = 745*(1.16)^4=
1,348.926
What is the correct method?

Question

Exponential growth formula: (1+r)^t or e^(r*t)?

A population of 745 quail increases at 16% per year. 
Write an exponential function for the quail population and  
what is the population be after 4 years?
I answered this question yesterday and said the answer was 745*e^(r*t) = 745*2.718281828^(.16*4) =
1,412.878
However, couldn't it also be solved by
745*(1+r)^t = 745*(1.16)^4=
1,348.926
What is the correct method?

marie2222 · Answer

745*e^rt

wolf1728 · Answer

Why does it produce 2 different answers?

vuriffy · Answer

It seems both of your methods are set up correctly.

vuriffy · Answer

Your e value is correct, so there is no issue there.

wolf1728 · Answer

I know when computing compound interest, the annual interest formula is 
(1+r)^t
But for continuously compound interest it is
e^(r*t)

vuriffy · Answer

Yes, that is true. We just need to differential your question for whichever one is classified for it.

marie2222 · Answer

You are dealing with animals and not interest

wolf1728 · Answer

Okay, so to put this in terms of the quail population, the 
e^(r*t) formula is different from the 
(1+r)^t formula in what way?

vuriffy · Answer

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