Question

a hot air balloons distance traveled, in miles, is given by the function $d(t) = 5.7t + 0.30$, where $t$ is measured in hours. interpret $d(3.2) = 18.54$.
after 3.2 hours, the hot air balloon traveled 5.7 miles
after 18.54 hours, the hot air balloon traveled 3.2 miles
after 3.2 hours, the hot air balloon traveled 18.54 miles
after 5.7 hours, the hot air balloon traveled 3.2 miles

Explanation:

Step1: Understand the function

The function \( d(t) = 5.7t + 0.30 \) represents the distance \( d \) (in miles) traveled by the hot air balloon in \( t \) hours. Here, \( t \) is the input (time in hours) and \( d(t) \) is the output (distance in miles).

Step2: Interpret \( d(3.2) \)

When we have \( d(3.2) \), the input \( t = 3.2 \) hours. We then calculate \( d(3.2) \) using the function, and we are told \( d(3.2)=18.54 \). This means that when the time \( t \) is 3.2 hours, the distance \( d \) traveled is 18.54 miles.

Answer:

After 3.2 hours, the hot air balloon traveled 18.54 miles.