seufangelShay
Answered

Over two summers, Ray saved $900 and $500. The polynomial 900x2 + 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?

A264%
B0.1%
C1.1%
D8.4%

Verified Answer :

HomertheGenius

900 x² + 500 x= 1600   /:100
9 x² + 5 x = 16
9 x² + 5 x - 16 = 0
x 1/2 =\(\frac{-5\pm \sqrt{5^{2}-4*9*16 } }{18} = \frac{-5\pm \sqrt{25+576} }{18}= \\ = \frac{-5+24.52}{18}\)
x = 1.084 
The interest rate:
r = x - 1 = 1.084 - 1 = 0.084 = 8.4 %
Answer: D) 8.4 %

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