Question

David takes out a 20year 70,000 loan from his bank 2010. The quadratic equation that approximates the year/loan balance relationship is y = - 98x ^ 2 - 1, 531x + 69, 71 , where x is the number of years and y is the balance In what year, will his loan balance be $37,2347

Answer 1

Answer:

2022

Step-by-step explanation:

The duration of the loan David takes = 20 year loan

The amount David takes as loan = 70,000

The year David takes the loan = 2010

The year/loan balance relationship is y = -98·x² - 1,531·x + 69,710 (We note that the proper constant for the loan balance should be approximately 70,000, therefore the added zero)

Where;

x = The number of yeas

y = The balance

The year his loan balance will be $37,234.7, is given as follows;

37,234.7 = -98·x² - 1,531·x + 69,710

-98·x² - 1,531·x + 69,710 - 37,234.7 = 0

-98·x² - 1,531·x + 32,475.3 = 0

Factorizing with a graphic calculator, gives;

-98·(x - 11.998)·(x + 27.62) = 0

∴ x = 11.998 ≈ 12 or -27.62

The number of years it takes for the loan balance to be $37,234.7 = 12 years

Given that he took the loan in 2010, the loan balance will be $37,234.7 in 2010 + 12 = 2022