Question 388750
Elly invested money in an account with a fixed interest rate. The interest is compounded annually. After 5 years her balance was $2741.69, and after 10 years her balance was $3416.53.
A.Find an exponential equation that models these data. (round the growth rate to thousandths.
A = amount invested, r = interest rate in decimal form
@ 5 yrs: 2741.69 = A*(1 + r)^5
@10 yrs: 3416.53 = A*(1 + r)^10
2 variables, 2 equations
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log(2714.69) = log(A) + 5*log(1+r)
log(3416.53) = log(A) + 10*log(1+r)
------------------------------------- Subtract 1 from 2
0.0999865 = 5*log(1+r)
log(1+r) = 0.019973
1+r = 1.04706
r =~ 4.7%
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B.How much did Elly orignally invest?
log(2714.69) = log(A) + 5*log(1+r)
log(A) = log(2714.69) - 5*log(1.047) = 3.3339868
A = $2157.68
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C.What is the interest rate for the account? 4.7%