a population of field mice is 120. The population increases at a rate of 9% a year. write an exponential function that models this situation?

Answer 1

A(t) = 120(1.09)^t

Questions?

Answer 2

m(t)= 120e^.09t

or

possibly 120(1.09)^t

but unless there's a mating season or similar reason why the increase occurs one time per year, rather than continuously, the 1st model is more realistic. They give about the same results. Things in nature, grow or decay "naturally" and continuous compounding for decay or growth models the situation more realistically.

general formula is

A=P(1+r/n)^nt where

P = starting number

A = ending number

r = annual growth or decay rate

t = number of years

n = number of compounding periods per year

for mice = 120(1.09)^t, that assumes 1 compounding period per year

as n approaches infinity

the formula becomes 120e^.09t

but there's little difference in A, for small time periods