Answer:
2.8%/month
Explanation:
We'll assume that f(t)=16(1.4)^t is the deer population in the forest as a function of time, x. ax is years after the starting year (when x = 0). 16 is the initial population at t = 0 (f(0)=16(1.4)^0 is equal to 16*1 or 16.
f(0) = 16
The 1.4 is telling us that the deer population increases by 40% each year. (1 + 40%, or 1.40).
The monthly rate would be written as f(x) = 16*(1+R)^x, where x is now in months and R is the percent increase each month. To find R, the monthly rate increase, let's calculate the population after 1 year in the original formula:
f(1) = 16*(1.4)^1 or 22.4
Now lets use that figure in the monthly equation for 12 months (1 year):
f(12) = 16*(1+R)^12
We already know that f(12) = 22.4:
22.4 = 16*(1+R)^12
R = 0.028 or 2.8%/month