Question

A runner is jogging at a constant speed of 3.6 miles per hour

a. Find the distance d that the runner jogs as a function of the time spent jogging t. Call this function d (t). Use an asterisk; for any multiplication and /, slash; for any division: d (t)
b. Find the inverse function by expressing the time spent jogging t in terms of the distance jogged d. Call this function t (d). Use an asterisk; for any multiplication and / , a slash; for any division. t (d)

Answer 1

The distance function for the runner is d(t) = 3.6 * t, which shows distance is proportional to time. The inverse function, representing time as a function of distance, is t(d) = d / 3.6.

Step-by-step explanation:

The function describing the distance d jogged by a runner as a function of the time t spent jogging is:

d(t) = 3.6 * t

To find the inverse function expressing the time t in terms of the distance d, we solve this function for t:

t(d) = d / 3.6

The inverse function t(d) allows us to calculate the time spent jogging based on a given distance jogged. To convert the speed back into time, simply divide the distance by the speed.