Question

The approximate length (in cm) of a typical Pacific halibut t years old is given by f(t) = 200(1 -0.956e-0.181).

A Pacific lialibut caught by Mike measures 140cm. What is its approximate age?​

Answer 1

6 years old

Explanation:

Given

`f(t) = 200(1 -0.956e^(-0.18t))`

Required

Find t when f(t) = 140cm

Substitute f(t) = 140cm

`140 = 200(1 -0.956e^(-0.18t))`

Divide both sides by 200

`0.7 = 1 -0.956e^(-0.18t)`

Collect like terms

`0.956e^(-0.18t) = 1 -0.7`

`0.956e^(-0.18t) = 0.3`

Solve for t

`e^(-0.18t) = 0.3/0.956`

`e^(-0.18t) = 0.31381`

Take natural logarithm of both sides

`ln(e^(-0.18t)) = ln(0.31381)`

`-0.18tln(e) = ln(0.31381)`

`-0.18t*1 = ln(0.31381)`

`-0.18t = -1.159`

Solve for t

`t = (-1.159)/(-0.18)`

`t = 6.43`

`t \approx 6`