Question

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linear application
the function $c(q)=39000-3000q$ represents the balance in your college payment account after $q$ quarters.
interpret the slope in this situation.
the balance in this account is decreasing at a rate of 3000 dollars per quarter
interpret the initial value in this situation.
after quarters, the balance in this account is $.
how many quarters will this account pay for?
you can pay for 13 quarters before the money in this account is gone.

Explanation:

Step1: Identify initial value (q=0)

$C(0) = 39000 - 3000(0) = 39000$

Step2: Interpret initial value

The initial account balance is $39000, the starting amount before any quarters of payments are made.

Step3: Find q when balance is $0

Set $C(q)=0$: $0 = 39000 - 3000q$

Step4: Solve for q

$3000q = 39000$
$q = \frac{39000}{3000} = 13$

Step5: Find balance at q=13

$C(13) = 39000 - 3000(13) = 39000 - 39000 = 0$

Answer:

• Interpret the Initial Value in this situation: The initial balance of the college payment account is $39000 (the amount available before any quarters of payments are made).
• After 13 quarters, the balance in this account is $0.
• How many quarters will this account pay for? 13