A ranch experienced growth of its gopher population at a 1.5% annual rate, compounded continuously. At the end of a 3 year period, the population had reached a size of 78 gophers. How many gophers were on the ranch at the beginning of the 3 years according to the exponential growth function? Round your answer up to the nearest whole number, and do not include units.

75 gophers (about)

Step-by-step explanation:

We will use continuous compounding interest formula:

Where

P(t) is final value (at time t)

P_0 is initial value

r is the compounding rate

t is the time period

Given:

P(t) = 78

r is 1.5% or 1.5/100 = 0.015

t is 3

We solve for P_0, what we want, using algebra as shown below:

So, the initial population was 75 gophers.

b

step-by-step explanation:

answer: a.

step-by-step explanation: the answer is a. because, you need to converge the fractions to find a solution.