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% my answer is C can someone plz tell me if it's correct

Question

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%	 my answer is C can someone plz tell me if it's correct

anonymous · Answer

$$ 900x^2 + 500x = 1600  \Rightarrow  900x^2 + 500x - 1600 = 0  $$
Use the quadratic equation to solve for $x$.  You will have two solutions.  Pick the most logical one (one that isn't negative.
Plug that into $x$ for  $r = x - 1$ to get $r$.

anonymous · Answer

ok so its A

anonymous · Answer

No.  C is the correct answer.
When we solve for $x$ we get $1.0842$ and a negative solution we can throw away.
So $r = 1.0842 - 1 = 0.0842$.  Now we change this into a percent and get $8.42 \% $

anonymous · Answer

ok

anonymous · Answer

I never meant to imply that C is incorrect.  I just wanted to make sure you knew the method.

anonymous · Answer

oh ok thank you you have been a big help