The speed, V (km/h), of a car at time t (seconds) is given by

where 0 ? t ? 60 (note the exponential function, ex, can be written as exp (x)).

1. We want to know when the car will reach a certain speed. Solve for the time t in terms of the speed V , and hence find the formula for the inverse function f^-1(t).

2. Write down the domain of f^?1(t).

3. Plot f(t) from t = 0 to t = 60 and then plot f^?1(t) on the same axes but only for the values of t in the domain of the inverse function found in (b).

4. Describe the geometric relationship that you can see when you consider both f(t) and f^?1(t).

V = f(t) = 50 + 15 exp ((t 40)/8000) 1 + exp ((t 40)/8000)