Question

For an average​ person, the rate of change of weight W​ (in pounds) with respect to height h​ (in inches) is given approximately by the following formula.
dW/dh=0.0018h^2

Find​ W(h) if ​W(80​)equals=287.2 pounds. ​ Also, find the weight of a person who is 5​ feet, 8 inches tall.

W(h)=_______

A Person who is 5 feet, 8 inches tall weighs about _______ lbs

Answer 1

Answer:

$W(h)=0.0006h^3-20$.

A Person who is 5 feet, 8 inches tall weighs about 168.7 lbs.

Step-by-step explanation:

We know the rate of change of weight W​ (in pounds) with respect to height h​ (in inches)

$\frac{dW}{dh}=0.0018h^2$

This is a separable equation. A separable equation is a first-order differential equation in which the expression for $\frac{dy}{dx}$ can be factored as a function of x times a function of y. In other words, it can be written in the form

$\frac{dy}{dx}=g(x)f(y)$

• To find W(h), we write the equation in terms of differentials and integrate both sides:

$\frac{dW}{dh}=0.0018h^2\\\\dW=(0.0018h^2)dh\\\\\int dW=\int (0.0018h^2)dh\\\\W=0.0006h^3+C$

To find the value of C, we use W(80​) = 287.2 lbs

$287.2=0.0006(80)^3+C\\0.0006\left(80\right)^3+C=287.2\\307.2+C=287.2\\307.2+C-307.2=287.2-307.2\\C=-20$

Thus,

$W(h)=0.0006h^3-20$

• To find the weight of a person who is 5​ feet, 8 inches tall you must:

Convert the 5 feet into inches

$5 \:ft \:\frac{12 \:in}{1\:ft} = 60 \:in$

Add 60 in and 8 in, to find the total height of the person

h = 68 in

Substitute h = 68 in into $W(h)=0.0006h^3-20$ to find the weight:$W(68)=0.0006(68)^3-20=168.7$

A Person who is 5 feet, 8 inches tall weighs about 168.7 lbs.