Answer:
3.75 months
Step-by-step explanation:
You want the number of months it takes to increase from 2500 to 3200 at the rate of 6.8% per month.
The exponential function describing the population can be written as ...
population = (initial number) × (growth factor)^n
where "growth factor" is the multiplier of the population for each time period. The growth factor is (1 + growth rate) = (1 + 6.8%) = 1.068.
We want to find n, the number of time periods required to make the population become 3200, if the initial number is 2500:
3200 = 2500 × 1.068^n
3200/2500 = 1.068^n . . . . . . . . . divide by 2500
log(32/25) = n·log(1.068) . . . . . . . take logarithms
n = log(32/25)/log(1.068) ≈ 3.7524
It will be about 3.75 months before there are 3200 rabbits.
