Question

A school basketball team has an expense account and a fundraising account. After t

weeks, the balance of the expense account is (450−70t)
dollars and the balance of the fundraising account is (275+48t)
dollars.

a. Write an expression in simplest form that represents the total amount (in dollars) in both accounts after t
weeks.
An expression is (725) dollars.

b. What is the total amount (in dollars) in both accounts after 9 weeks?

Amount after 9 weeks: $

Answer 1

1) the expression that gathers the expenses and the income is the utility function and is defined by U(t) = I(t)-G(t), where I(t) is income and G(t) is expenses, the simplest form that represents the total amount of the balance of the expense account is, for this exercise I(t) = 275+48t and G(t) = 450-70t

PART A

U(t)= 275+48t-(450-70t) ⇒U(t) = 275+48 t-450+70t⇒U(t) = 118t -175

PART B

For f(t) = (275+48t) the total amount (in dollars) after 9 weeks?

it is f(9) = [(450 - 70(9)]= $220

for f(t) =275 +48t ,the total amount in dollars after 9 weeks is f(9) = 275+48(9) = $ 707