Question

A certain population of mice is growing exponentially. After one month there are 48. After 2 months there are "192" mice. Write an equation that represents this scenario(With work)

Answer 1

P(t) = 12e^1.3863k

Explanation:

The general exponential equation is represented as;

P(t) = P0e^kt

P(t) is the population of the mice after t years

k is the constant

P0 is the initial population of the mice

t is the time in months

If after one month there are 48 population, then;

P(1) = P0e^k(1)

48 = P0e^k ...... 1

Also if after 2 months there are "192" mice, then;

192 = P0e^2k.... 2

Divide equation 2 by 1;

192/48 = P0e^2k/P0e^k

4 = e^2k-k

4 = e^k

Apply ln to both sides

ln4 = lne^k

k = ln4

k = 1.3863

Substitute e^k into equation 1 to get P0

From 1, 48 = P0e^k

48 = 4P0

P0 = 48/4

P0 = 12

Get the required equation by substituting k = 1.3863 and P0 = 12 into equation 1, we have;

P(t) = 12e^1.3863k

This gives the equation representing the scenario