Question

A tank contained 80 liters of water. The function “w” represents the relationship between “t”, time in minutes, and the amount of water in the tank in liters. The equation w(t) = 80 - 2.8t defines this function. How would the graph of the inverse function of compare to the graph of “w”? PLEASE HELP!!

Answer 1

w(t) tells you the amount of water w at a given time t.

The inverse function tells you at which time t the tank contains an amount of water w.

To get the inverse function, solve the equation

w = 80 - 2.8t

for t :

w = 80 - 2.8t

2.8t = 80 - w

t = (80 - w) / 2.8

t ≈ 28.57 - 0.357 w

The graph of w(t) is a downward-sloping line. The graph of the inverse is also a downward-sloping line, but its intercept (28.57) and slope (-0.357) are both smaller than the intercept and slope of w(t).