Question

Researchers find that there are 70 Raccoons on an island. When they return a year later, they find that there are 84. Assuming an exponential growth pattern, what is the annual population growth factor for the raccoons?

A. 0.2
B. 1.2
C. 0.8
D. 1.4

Answer 1

The annual population growth factor for the raccoons is 0.2.

Step-by-step explanation:

To determine the annual population growth factor of the raccoons, we can use the exponential growth formula:

P(t) = P0 * (1 + r)^t

Where:

P(t) is the population at time t,

P0 is the initial population,

r is the annual growth rate as a decimal,

t is the number of years.

In this case, the initial population P0 is 70, and the population after one year P(1) is 84. We can substitute these values into the formula:

84 = 70 * (1 + r)^1

Simplifying the equation:

(1 + r) = 84/70

1 + r = 12/10

r = 12/10 - 1

r = 0.2

Thus, the annual population growth factor for the raccoons is 0.2.