Question

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 ____ quarters before the money in this account is gone.

Explanation:

Step1: Interpret slope of linear function

The slope is $-3000$, so the balance decreases by $\$3000$ per quarter.

Step2: Interpret initial value (q=0)

Substitute $q=0$ into $C(q)=39000-3000q$:
$C(0)=39000-3000(0)=39000$
This is the starting balance.

Step3: Find quarters until balance is $0$

Set $C(q)=0$ and solve for $q$:
$0=39000-3000q$
$3000q=39000$
$q=\frac{39000}{3000}=13$

Answer:

Interpret the Slope: The balance in this account is decreasing at a rate of 3000 dollars per quarter.
Interpret the Initial Value: The initial balance (when $q=0$ quarters) is $\$39000$.
How many quarters will this account pay for? 13 quarters
You can pay for 13 quarters before the money in this account is gone.