You 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 $1500.00 1 $1518.00 2 $1536.22 3 $1554.65 4 $1573.31 5 $1592.19 (a) Show that the data are exponential. (Round your answer to three decimal places.) Each successive ratio of new/old is _______, 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) = (b) What is the monthly interest rate? (Round your answer to one decimal place.) _________% (c) What is the yearly interest rate? (Round your answer to one decimal place.) ________%
You 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 $1500.00 1 $1518.00 2 $1536.22 3 $1554.65 4 $1573.31 5 $1592.19 (a) Show that the data are exponential. (Round your answer to three decimal places.) Each successive ratio of new/old is _______, 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) = (b) What is the monthly interest rate? (Round your answer to one decimal place.) _________% (c) What is the yearly interest rate? (Round your answer to one decimal place.) ________%
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
You 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.
(a) 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.)
(b) What is the monthly interest rate? (Round your answer to one decimal place.)
_________%
(c) What is the yearly interest rate? (Round your answer to one decimal place.)
________%
(d) 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 19. How large a college fund will she have? (Round your answer to the nearest cent.)
$_________
(e) How long does it take your money to double in value? (Round your answer to two decimal places.)
__________months
How much longer does it take it to double in value again? (Round your answer to two decimal places.)
_________months
| Time in months |
Savings balance |
|---|---|
| 0 | $1500.00 |
| 1 | $1518.00 |
| 2 | $1536.22 |
| 3 | $1554.65 |
| 4 | $1573.31 |
| 5 | $1592.19 |
(a) Show that the data are exponential. (Round your answer to three decimal places.)
Each successive ratio of new/old is _______, 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) =
(b) What is the monthly interest rate? (Round your answer to one decimal place.)
_________%
(c) What is the yearly interest rate? (Round your answer to one decimal place.)
________%
(d) 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 19. How large a college fund will she have? (Round your answer to the nearest cent.)
$_________
(e) How long does it take your money to double in value? (Round your answer to two decimal places.)
__________months
How much longer does it take it to double in value again? (Round your answer to two decimal places.)
_________months
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