Question

The weight W in ounces of a certain small mammal is proportional to the cube of its length L in
inches. The length in inches of the animal depends on its age t in years.

The relationship is as follows:
L = 8(1-e^-t)
(a) Express W as a function of t using c as the constant of proportionality.
(b) It is found that a 3-year-old animal weighs 17 ounces. Find the value of c.

Answer 1

w = c L^3

w = c [512] [ (1-e^-t)^3 ]

= 512 c

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aside multiplication problem
(1-e^-t)^3 = (1-e^-t)(1 - 2e^-t +e^-2t)
=1(1 - 2e^-t +e^-2t)
-e^-t(1 - 2e^-t +e^-2t)
= 1 - 2e^-t +e^-2t -e^-t +2e^-2t -e^-3t
= 1 -3e^-t +3e^-2t -e^-3t
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w = 512 c [1 -3e^-t +3e^-2t -e^-3t]
put in t = 3 and w = 17 and get c
of course you would say c'=512 c
in real life