Question

A marathon runner will donate $5000 to charity if her time is less than or equal to 3 hours. She will donate $2000 if her time is more than 3 hours but less than or equal to 4 hours. Finally, she will donate $1000 to charity if her time is more than 4 hours.

a. Write a piecewise function describing this situation.

Answer 1

5000>3>2000>4>1000 hope this helps

Answer 2

`f(x)=\left\{\begin{matrix}5000, & 0\leq x\leq 3 \\ 2000, & 3 < x \leq 4 \\ 1000 & 4<x\end{matrix}\right.`

Explanation:

Let x represents the number of hours and f(x) represents the amount ( in dollars ) of donation for x hours,

Given,

for x ≤ 3,

f(x) = 5000,

For 3 < x ≤ 4,

f(x) = 2000,

For 4 < x,

f(x) = 1000,

∵ Number of hours can not be negative,

⇒ x ≥ 0

Hence, the required function is,

`f(x)=\left\{\begin{matrix}5000, & 0\leq x\leq 3 \\ 2000, & 3 < x \leq 4 \\ 1000 & 4<x\end{matrix}\right.`