Question

The length (in centimeters) of a typical Pacific halibut t years old is approximately
f(t) = 190(1 − 0.955e−0.25t).


(b) How fast is the length of a typical 9-year-old Pacific halibut increasing?
cm/yr

(c) What is the maximum length a typical Pacific halibut can attain?
cm

Answer 1

You sure are having quite a time with these exponential functions!

y = 190 [ 1- .955 e^-(.25 t) ]

If t = 9
y = 190 [ 1 - .955(.105) ]
= 190 [ 1 - .1 ]
= 171 cm
In other words it has reached 90% of max length in 9 years
now
dy/dt = 190(-.955) (-.25)(.105)
= 4.76 cm/year

c) when t gets very large e^-.25 t = 1/e^oo = 0
so
max length = (190)(1) = 190 cm