Question

Researchers find that there are 173 raccoons on an island. When they return a year later, they find that there are 413. Assuming an exponential growth in population, what is the annual population growth factor for the raccoons?Express your answer as a decimal, rounded to the nearest hundredth.

Answer 1

Population growth formula

`P=P_0*e^(rt)`

where,

P = total population after time t,

P0 = initial population

r = rate of growth

t = time in years

Given,

P0 = 173

P = 413

t = 1 year

Solution process,

let's replace and solve for r,

`413=173*e^(r*1)`
`\begin{gathered} e^r=(413)/(173) \\ \end{gathered}`

apply exponent rules,

`r=\ln \left((413)/(173)\right)`

Therefore, r=0.87015

Rounding to the nearest hundredth, r = 0.87