Julieta has been in the car with her family on a road trip for the past three hours. For the first hour, they went about 55 mph. Then, the speed limit changed and they started going about 70 mph. They are still going 70 mph.

Question

Create a piecewise function that models the distance Julieta's family has
traveled over time.

MAKE THE ANSWER SHORT PLEADE

Answer 1

Let \( t \) be the time in hours since they started the trip. The piecewise function \( D(t) \), representing the distance traveled in miles, can be defined as:

\[ D(t) = \begin{cases} 55t & \text{for } 0 \leq t < 1 \ 55 + 70(t - 1) & \text{for } 1 \leq t \leq 3 \ \end{cases} \]

This function accounts for the first hour of travel at 55 mph and the following hours at 70 mph.