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: $

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