Question

The length (in centimeters) of a typical Pacific halibut t years old is approximately f(t) = 200(1 − 0.956e−0.18t). Suppose a Pacific halibut caught by Mike measures 148 cm. What is its approximate age? (Round your answer to one decimal place.)

Answer 1

Answer:

7.2 years

Step-by-step explanation:

$f(t) =200(1 - 0.956e^{-0.18t})$

where f(t) is the length and t is the number of years old

given the Mike measures 148 cm, we need to find out the age

So we plug in 148 for f(t) and solve for t

$148 =200(1 - 0.956e^{-0.18t})$

divide both sides by 200

$\frac{148}{200} = 1 - 0.956e^{-0.18t}$

Now subtract 1 from both sides

$-0.26= - 0.956e^{-0.18t}$

Divide both sides by -0.956

$\frac{0.26}{0.956} =e^{-0.18t}$

Now take ln on both sides

$\frac{0.26}{0.956} =e^{-0.18t}$

$ln(\frac{0.26}{0.956} )=-0.18tln(e)$

$ln(\frac{0.26}{0.956} )=-0.18t$

divide both sides by -0.18

t=7.2

So 7.2 years