SOLUTION: Over two summers, Ray saved $900 and $500. The polynomial 900x^2 + 500x represents his savings at the beginning of the third year, where x is the growth factor. (The interest rate

Question 707190: Over two summers, Ray saved $900 and $500. The polynomial 900x^2 + 500x represents his savings at the beginning of the third year, where x is the growth factor. (The interest rate r is x - 1.) What is the interest rate he needs to start the third year with $1600 in savings?
A. 1.1%

B. 0.1%

C. 8.4%

D. 264%
(show all work please)
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
We're told that "The polynomial 900x^2 + 500x represents his savings at the beginning of the third year" and "the third year with $1600 in savings", so

900x^2 + 500x = 1600

Solve for x

900x^2 + 500x = 1600

900x^2 + 500x - 1600 = 0

Use the quadratic formula to solve for x

Plug in , ,

or

or <--- Use your calculator here ( solutions are approximate and not exact)

Toss out the negative solution because you can't have a negative interest rate.

So the only approximate solution is

So because r = x - 1 is the interest rate, we know that the interest rate is

r = x - 1

r = 1.084183 - 1

r = 0.084183

Which is equivalent to 8.4%
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