Question

A wolf population is growing exponentially. In 2011, 129 wolves were counted. By 2013 the population had reached 236 wolves. Find the multiplier (round to the nearest hundredth)

Answer 1

Given:

Number of wolves in 2011 = 129

Number of wolves in 2013 = 236

To Find:

The multiplier

Solution:

Find the number of years past:

Find the number of years = 2013 - 2011

Find the number of years = 2

Find the multiplier:

Let the multiplier be M

$\text{Number of years at 2013} = \text{Number of years at 2011} ( 1 + \text{Multiplier}) ^2$

$236 = 129 ( 1 + \text{M}) ^2$

$236 = 129 ( 1 + \text{M}^2 + 2M) ^2$

$236 = 129+ 129\text{M}^2 + 258M$

$129\text{M}^2 + 258M - 107 = 0$

$M = 0.353 \text{ or } M = -2.353 \text{(Rejected)}$

Find the multiplier as a percentage:

multiplier = 0.353 x 100

multiplier = 35.3%

Answer: The multiplier is  35.3%

Answer 2

Answer:

the multiplier is 35.3