Word Problem: finding lung volume, given height and age

Radar

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Apr 20, 2006
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The question is:

The volume of air an adult's lungs can hold decreases with age. The equation

V = 0.104h - 0.018a - 2.69 gives an estimate of the V(in liters) of a person's lungs for someone of height h inches and and age a years.

A. Using your own height (64) and and weight (155) in the above, calculate your estimated lung volume.

B. Calculate 90% of your lung volume.

C. Solve the equation above for the variable a.

D. Calculate how old you will be when your air volume is 90% of its current value. (Use your current height.)
 
a. V = 0.104(h) - 0.018(a) - 2.69
V = 0.104(64) - 0.108(53) - 2.69
V = 6.656 - 0.954 - 2.69
V = 3.012

b. 3.012/90
2.7108

c. 6.656 - 3.012 - 2.69 = 0.954
0.954 = 0.018a
a = 53

d. 2.7108 = 6.656 - 2.69 - 0.018a
6.656 - 2.7108 - 2.69 = 1.2552
1.2552 = 0.018a
a = 69.5
 
Something a little haywire on this one.

Are we using weight or age? I'm confused.

A coefficient changed from 0.018 to 0.108. That can't be good. Negative lung capacity is not useful. :(

"Solve for 'a'" means rearrange the formula so that 'a' is alone. it does NOT mean to substitute given values. Like this.

V = 0.104*h - 0.018*a - 2.69
V + 2.69 = 0.104*h - 0.018*a
V + 2.69 - 0.104*h = - 0.018*a
(V + 2.69 - 0.104*h)/(-0.018) = a

or you can rearrange it a bit

a = (0.104*h - 2.69 - V)/0.018

Try those again.
 
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