Question

optional - ungraded ch 3 practice quiz
score: 1/40 answered: 1/7
question 2
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 increasing at a rate of quarters
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: Analyze slope of linear function

The function is $C(q) = 39000 - 3000q$, which follows the form $y = mx + b$ where $m$ is slope. Here, $m = -3000$. Since the slope is negative, the balance is decreasing at a rate of $\$3000$ per quarter.

Step2: Interpret initial value

The initial value is the $y$-intercept $b$, which occurs when $q=0$.
$C(0) = 39000 - 3000(0) = 39000$
This is the account balance at 0 quarters.

Step3: Find balance after 0 quarters

When $q=0$, $C(0) = 39000$.

Step4: Find total quarters until balance is 0

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

Answer:

• The balance in this account is decreasing at a rate of $\boldsymbol{3000}$ dollars per quarter.
• The initial value is the account balance of $\boldsymbol{\$39000}$ when 0 quarters have passed.
• After $\boldsymbol{0}$ quarters, the balance in this account is $\boldsymbol{\$39000}$.
• You can pay for $\boldsymbol{13}$ quarters before the money in this account is gone.