Question

The distance traveled, in miles, as a function of time, in hours, is defined by D(t).

D(t) =

Which times and distances are represented by the function?
Check all that apply.

The starting distance, at 0 hours, is 300 miles.

By 2 hours, the distance traveled is 725 miles.

At 2.5 hours, the distance traveled is 875 miles.

At 3 hours, the distance is constant, at 880 miles.

The total distance traveled in 6 hours is 1,062.5 miles.

Answer 1

Options B, D, E are correct.

Explanation:

We will check the statements of every option for the given function.

A). The starting distance, at 0 hours is 300 mles.

D(t) = 300t + 125 0 ≤ t < 2.5

D(0) = 125 miles

Therefore option is not correct.

B). By 2 hours, the distance traveled is 725 miles.

D(t) = 300t + 125 0 ≤ t ≤ 2.5

D(2) = 300×2 + 125 = 600 + 125 = 725 miles

Therefore Option B is correct.

C) At 2.5 hours, the distance traveled is 875 miles.

D(t) = 880 2.5 ≤ t ≤ 3.5

Therefore option C is not correct.

D). At 3 hours, the distance is constant, at 880 miles

D(t) = 800 2.5 ≤ t ≤ 3.5

Therefore Option D. is correct

E). The total distance traveled in 6 hours is 1062.5 miles.

D(t) = 75t + 612.5 3.5 < t ≤ 6

D(6) = 75×6 + 612.5 = 450 + 612.5 = 1062.5 miles.

Option E is also correct.

Options B, D, E are correct.