Question

A population of bears increased by 50% in 4 years. If the situation is modeled by an annual growth rate compounded continuously, which formula could be used to find the annual rate according to the exponential growth function? Leave your answer in terms of ln.

Answer 1

Answer:

$r=\frac{ln(1.5)}{4}$

Explanation:

Given:

Total population after time (P) = 100% + 50%  = 1 + 0.5 = 1.5

Starting population (p) = 100% = 1

Number of year (t) = 4 year

rate of growth = r

Computation:

Exponential growth function for population :

P = $pe^{rt}$

1.5 = $1\times e^{4\times r}$

1.5 = $e^{4r}$

From taking log:

4r = ln(1.5)

$r=\frac{ln(1.5)}{4}$