Shay works each day and earns more money per hour the longer she works. Write a function to represent a starting pay of $20 with

Question

riadik2000 [5.3K]

3 years ago

14

Shay works each day and earns more money per hour the longer she works. Write a function to represent a starting pay of $20 with

an increase each hour by 4%. Determine the range of the amount Shay makes each hour if she can only work a total of 8 hours.
A.20 ≤ x ≤ 22.51
B.20 ≤ x ≤ 25.30
C.20 ≤ x ≤ 26.32
D.20 ≤ x ≤ 27.37

Mathematics

2 answers:

Masja [62] · Answer 1 · 2022-06-29T04:28:54+03:00

Answer:

<u>Function</u>: $p(x)=20(1.04)^x$

<u>Range</u>: option D. 20 ≤ x ≤ 27.37

Explanation:

The function must meet the rule that the pay starts at $20 and it increases each hour by 4%.

A table will help you to visualize the rule or pattern that defines the function:

x (# hours) pay ($) = p(x)

0 20 . . . . . . . . [starting pay]

1 20 × 1.04 . . . [ increase of 4%]

2 20 × 1.04² . . . [increase of 4% over the previous pay]

x 20 × 1.04ˣ

Hence, the function is: $p(x)=20(1.04)^x$

The range is the set of possible outputs of the function. To find the range, take into account that this is a growing exponential function, meaning that the least output is the starting point, and from there the output will incrase.

The choices name x this output. Hence, the starting point is x = 20 and the upper bound is when the number of hours is 8: 20(1.04)⁸ = 27.37.

Then the range is from 20 to 27.37 (dollars), which is represented by 20 ≤ x ≤ 27.37 (option D from the choices).