You initially invest $400 in a savings account that pays a yearly interest rate of 3%. (a) Write a formula for an exponential function giving the balance your account as a function of the time since your initial investment. (Let 8 be the account balance in dollars and t be the number of years since the initial investment.) dollars B(t)= (b) What monthly interest rate best represents this account? Round your answer to three decimal places. % (c) Calculate the decade growth factor. (Round your answer to two decimal places.) (d) Use the formula you found in part (a) to determine how long it will take for the account to reach $536. (Round your answer to the nearest whole number.)
You initially invest $400 in a savings account that pays a yearly interest rate of 3%. (a) Write a formula for an exponential function giving the balance your account as a function of the time since your initial investment. (Let 8 be the account balance in dollars and t be the number of years since the initial investment.) dollars B(t)= (b) What monthly interest rate best represents this account? Round your answer to three decimal places. % (c) Calculate the decade growth factor. (Round your answer to two decimal places.) (d) Use the formula you found in part (a) to determine how long it will take for the account to reach $536. (Round your answer to the nearest whole number.)
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter7: Exponents And Exponential Functions
Section7.8: Transforming Exponential Expressions
Problem 18PFA
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Question
![You initially invest $400 in a savings account that pays a yearly interest rate of 3%.
(a) Write a formula for an exponential function giving the balance in your account as a function of the time since your initial investment. (Let B be the account balance in dollars and t be the number of years since the initial investment.)
dollars
B(t) =
(b) What monthly interest rate best represents this account? Round your answer to three decimal places.
%
(c) Calculate the decade growth factor. (Round your answer to two decimal places.)
(d) Use the formula you found in part (a) to determine how long it will take for the account to reach $536. (Round your answer to the nearest whole number.)
yr
Explain how this consistent with your answer to part (c).
At the end of one decade, there will be $
answer found above where the account reaches $536 at the end of
years.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcf03ac0f-3652-4fe4-83f1-0fd7d3580b95%2Fb3dc6d91-372a-45fd-9f93-5e83df77beb7%2Ftakt3w7_processed.png&w=3840&q=75)
Transcribed Image Text:You initially invest $400 in a savings account that pays a yearly interest rate of 3%.
(a) Write a formula for an exponential function giving the balance in your account as a function of the time since your initial investment. (Let B be the account balance in dollars and t be the number of years since the initial investment.)
dollars
B(t) =
(b) What monthly interest rate best represents this account? Round your answer to three decimal places.
%
(c) Calculate the decade growth factor. (Round your answer to two decimal places.)
(d) Use the formula you found in part (a) to determine how long it will take for the account to reach $536. (Round your answer to the nearest whole number.)
yr
Explain how this consistent with your answer to part (c).
At the end of one decade, there will be $
answer found above where the account reaches $536 at the end of
years.
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