Question 289971
A water tank containing 68 gallons of water had the drain opened. The water drains out at 3 gallons per minute. Let g=f(t) be the function that gives the number of gallons of water (g) remaining in the tank t minutes after the drain is opened.
a. Give an equation which describes this function.
f(t) = 68 - 3t
That is:
f(t) = "amt of water at start" - "amt of water drained for t minutes"
.
b. Explain how to evaluate and interpret f(13)
f(t) = 68 - 3t
f(13) = 68 - 3(13)
f(13) = 68 - 39
f(13) = 29 gallons
After 13 minutes, with the drain opened, there are 29 gallons of water left in the tank.


C. Explain how to evaluate and interpret f-1(20). f-1 meaning inverse.
f(t) = 68 - 3t
y = 68 - 3t
t = 68 - 3y
t - 68 = -3y
68 - t = 3y
y = 68/3 - t/3
f^1(t) = 68/3 - t/3
f^1(20) = 68/3 - 20/3
f^1(20) = 48/3 = 16 minutes
.
The original function:
f(t) = 68 - 3t
Given t (time) it predicts the amount of gallons in the tank
whereas the inverse:
f^1(g) = 68/3 - g/3
Given g (gallons) it predicts the amount of time it takes to drain to this vol