ou have invested money in a savings account that pays a fixed monthly interest on the account balance. The following table shows the account balance over the first 5 months. Time in months Savings balance 0 $1600.00 1 $1628.80 2 $1658.12 3 $1687.97 4 $1718.35 5 $1749.28 (a) How much money was originally invested?
ou have invested money in a savings account that pays a fixed monthly interest on the account balance. The following table shows the account balance over the first 5 months. Time in months Savings balance 0 $1600.00 1 $1628.80 2 $1658.12 3 $1687.97 4 $1718.35 5 $1749.28 (a) How much money was originally invested?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 13DE
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ou have invested money in a savings account that pays a fixed monthly interest on the account balance. The following table shows the account balance over the first 5 months.
| Time in months |
Savings balance |
|---|---|
| 0 | $1600.00 |
| 1 | $1628.80 |
| 2 | $1658.12 |
| 3 | $1687.97 |
| 4 | $1718.35 |
| 5 | $1749.28 |
(a) How much money was originally invested?
$ 1600.00
(b) Show that the data are exponential. (Round your answer to three decimal places.)
Find an exponential model for the account balance. (Let t be the time in months and B the savings balance in dollars. Round your parameters to three decimal places.)
(c) What is the monthly interest rate? (Round your answer to one decimal place.)
%
(d) What is the yearly interest rate? (Round your answer to one decimal place.)
%
(e) Suppose that you made this investment on the occasion of the birth of your daughter. Your plan is to leave the money in the account until she starts college at age 17. How large a college fund will she have? (Round your answer to the nearest cent.)
$
just need C,D, and E answered
$ 1600.00
(b) Show that the data are exponential. (Round your answer to three decimal places.)
Each successive ratio of new/old is 1.018, which shows that the data is exponential.
Find an exponential model for the account balance. (Let t be the time in months and B the savings balance in dollars. Round your parameters to three decimal places.)
B(t) =
1600.00·1.018t
(c) What is the monthly interest rate? (Round your answer to one decimal place.)
%
(d) What is the yearly interest rate? (Round your answer to one decimal place.)
%
(e) Suppose that you made this investment on the occasion of the birth of your daughter. Your plan is to leave the money in the account until she starts college at age 17. How large a college fund will she have? (Round your answer to the nearest cent.)
$
just need C,D, and E answered
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