Question

Ashton works as a marketing manager for a consumer products firm. His total earnings, A, in x months is given by the function A(x) = 2,400x + 40x2. His total savings, S, in x months is given by the function S(x) = 250x + 500.

The function E(x) = __________represents Ashton’s total expenses in x months.

Ashton’s expenses for 3 years total $________

Answer 1

Okay, so Ashton's expenses, of the amount of money he spends, is the amount of money he makes minus the amount of money he saves. So
E(x) = A(x) - S(x) = 2400x + 40x^2 - (250x + 500) = 40x^2 + 2150x - 500

This function represents his total expenses for x months, so we can simply plug 3 years, or 36 months, into this equation to get his total expenses:
E(36) = 40*(36^2) + 2150*36 + 500 = 51840 + 77400 - 500 = 128740

Answer 2

okay thank you!!

Answer 3

could you help me with one more?

Answer 4

@Blacksteel

Answer 5

Probably

Answer 6

A company has two packaging machines in a unit, each with a different daily capacity. The capacity of machine 1 is defined by the function f(m) = (m + 4)2 + 100, and the capacity of machine 2 is defined by the function g(m) = (m + 12)2 − 50, where m is the number of minutes the packaging machine operates. Create the function C(m) that represents the combined capacity of the two machines.

Answer 7

@Blacksteel

Answer 8

Machine 1's capacity is defined by f(m) = (m+4)^2 + 100 = m^2 + 8m + 16 + 100 = m^2 + 8m + 116

Machine 2's capacity is defined by g(m) = (m+12)^2 - 50 = m^2 + 24m + 144 - 50 = m^2 + 24m - 94

Then the capacity of both machines is given by h(m) = f(m) + g(m) = m^2 + 8m + 116 + m^2 + 24m - 94 = 2m^2 + 32m + 22

Answer 9

thank you! @Blacksteel