Amarathon 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.

Step-by-step 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,

option 3 . (5x + 1) - (-10x + 6)

step-by-step explanation:

option 1 :

(4x + 3) + (-9x + 4)

or 4x+3 -9x + 4

or -5x + 7

option 2

(x - 2) - (6x - 9)

or x-2-6x + 9

or -5x + 7

option 3

(5x+ + 6)

or 5x + 1 + 10x -6

or 15x -5

option 4

-4x+2x+7-3x

-7x + 2x + 7

-5x + 7

hence only option 3 did   not satisfy the given simplify expression.