SOLUTION: 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.

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.)
B.How much did Elly orignally invest?
C.What is the interest rate for the account?
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
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
---------------
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%
---------------
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
--------------------
C.What is the interest rate for the account? 4.7%
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