Question

A tank has 55 gallons of water in it. The water drains from the tank at the rate of 3 gallons per minute. The function f(x) models the number of gallons of water in the tank after x minutes. Find f^-1(15) and explain what it represents.

Please help!!!!

Answer 1

Explanation:

The initial amount is 55 gallons, and the rate is -3 gal/min. So using slope-intercept form, the equation is:

f(x) = -3x + 55

To find the inverse function, switch x and y, then solve for y.

x = -3y + 55

3y = -x + 55

y = (-x + 55) / 3

f⁻¹(x) = (-x + 55) / 3

Evaluated at x = 15:

f⁻¹(15) = (-15 + 55) / 3

f⁻¹(15) = 40 / 3

The original function told us number of gallons f(x) at time x.

The inverse function tells us time f⁻¹(x) at number of gallons x.

So there are 15 gallons in the tank after 40/3 minutes, or 800 seconds.