Question 1148013: The length (in centimeters) of many common commercial fish t years old can be approximated by a von Bertalanffy growth function having an equation of the form
f(t) = a[1 − be^−(kt)], where a, b, and k are constants.
(a) For Pacific halibut, a = 200, b = 0.956, and k = 0.18. Estimate the length of a 13-year-old halibut.
(b) Use the graph of f to estimate the maximum attainable length of the Pacific halibut.
cm
Answer by ikleyn(52800)   (Show Source):
You can put this solution on YOUR website! .
(a) Part (a) assumes that YOU substitute the given values to the formula and then YOU will use your calculator
or your computer to complete the assignment on your own.
There is nothing for tutors to do for you in this part ------- it is PURELY YOUR work.
(b) Part (b) assumes that you will use your pocket graphing calculator, or plotting utility in your computer,
or plotting ONLINE software in some Internet site and, again, will complete the assignment on your own.
As a tutor, I can recommend you to use (FREE of CHARGE) utility of the site https://www.desmos.com/calculator for plotting.
Also, as a tutor, I can help you to analyse the formula and to get the answer even WITHOUT making a plot.
After some years (many years or several years, 7 - 10 - 13 years) the term  becomes small and even VERY small;
so small that we can NEGLECT it.
Hence, the term  becomes small, and we can neglect it.
Then what remains is simply the term "a", which says us that the maximum attainable length of the fish
after several years becomes very close to the value of a = 200 cm = 2 meters.
It is the answer that I expect to (b).
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