SOLUTION: Suppose that your foot length L in inches is related to your height h in inches by L = (4/3)sqrt(h). In one (non-leap) year you have a growth spurt in which you grow from 64 inches

Question 1027563: Suppose that your foot length L in inches is related to your height h in inches by L = (4/3)sqrt(h). In one (non-leap) year you have a growth spurt in which you grow from 64 inches to 69 inches. Assume that your height changes at a constant rate throughout the year.
A) Find an expression for dL/dt.
B) What was the fastest rate of growth that your foot experienced during this time? When did it occur?
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
This is a related rates problem
:
(69 - 64) / 365 = 1/73
:
dh/dt = 1/73 inch/day
:
L = (4/3) * h^(1/2)
:
dL/dt = (2/3) * h^-(1/2) * dh/dt
:
dL/dt = (2/3) * h^-(1/2) * 1/73
:
*****************************
dL/dt = (2/219) * h^-(1/2)
*****************************
:
dL/dt decreases from day 1 to day 365
:
here is a graph of dL/dt
:

:
for h = 64 we have dL/dt = 0.001141553 approx 0.00114 inches/day
for h = 69 we have dL/dt = 0.001099414 approx 0.00109 inches/day
:

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