Vanessa purchased a smart TV for $1,500 on a payment plan. Four months after purchasing the TV, her balance was $1,200. 7 months after purchasing the TV, her balance was $975. Find an equation that models the balance B(t) after t months. How many months will it take her to pay off the TV loan?

The expression for her balance is "B(t) = -75*t + 1500". It'll take her 20 months to pay off the loan.

Step-by-step explanation:

We are looking for a function that has the following points:

B(0) = 1500

B(4) = 1200

B(7) = 975

Between B(4) and B(7), there was a variation of 3 months and a variation of -225 on her balance, thefore for each month that passed there was a variation of -75. Thefore, the expression for her ballance is:

B(t) = -75*t + 1500

To check if this expression is valid, we will apply the values provided on the problem:

B(0) = -75*0 + 1500 = 1500 (valid)

B(4) = -75*4 + 1500 = -300 + 1500 = 1200 (valid)

B(7) = -75*7 + 1500 = -525 + 1500 = 975 (valid)

When she pays of her loan, B(t) = 0, so we need to solve for t as shown below:

B(t) = -75*t + 1500 = 0

-75*t + 1500 = 0

75*t = 1500

t = 1500 / 75 = 20 months

It'll take her 20 months to pay the loan.