Question

arianna enjoys hiking at different parks. today, she will hike a 10-mile trail at catskill state park. she plans to use her smartwatch to help her maintain a steady pace of 2.5 miles per hour, which will allow her to complete the hike in 4 hours. the function d(t) represents the distance arianna has hiked, in miles, after t hours of hiking.
what is the range of d(t)?
all whole numbers from 0 to 2.5
all whole numbers from 0 to 5
all real numbers from 0 to 10
all real numbers from 0 to 5

Explanation:

Step1: Define the distance function

$D(t) = 2.5t$

Step2: Identify valid time range

$0 \leq t \leq 4$

Step3: Calculate min/max distance

Minimum: $D(0) = 2.5(0) = 0$
Maximum: $D(4) = 2.5(4) = 10$

Step4: Determine range type

Distance can take any value between 0 and 10 (not just whole numbers), so it includes all real numbers in this interval.

Answer:

all real numbers from 0 to 10