Suppose you make a charge of $1000 to a new credit card, but then charge nothing else and make the minimum payment each month. If the finance charges amount to a monthly rate of 1% and the minimum payment is 6% of the new balance, then your balance B, in dollars, after n payments is an exponential function given by the following formula. B = 1000 x an Here the decay factor a is obtained from the finance charge and the minimum payment as shown in the following formula. a = (1 + 0.01)(1 – 0.06) (a) Find the exact value of the decay factor a. (Round your answer to three decimal places.) (b) By what percentage does your balance decrease each month? (Round your answer to one decimal place.) (c) What will your balance be after you have made payments for 1 years? (Round your answer to two decimal places.)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.2: Exponential Functions
Problem 56E
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Suppose you make a charge of $1000 to a new credit card, but then charge
nothing else and make the minimum payment each month. If the finance
charges amount to a monthly rate of 1% and the minimum payment is 6% of
the new balance, then your balance B, in dollars, after n payments is an
exponential function given by the following formula.
B = 1000 x an
Here the decay factor a is obtained from the finance charge and the minimum
payment as shown in the following formula.
a = (1 + 0.01)(1 – 0.06)
(a) Find the exact value of the decay factor a. (Round your answer to
three decimal places.)
(b) By what percentage does your balance decrease each month? (Round
your answer to one decimal place.)
(c) What will your balance be after you have made payments for 1 years?
(Round your answer to two decimal places.)
$
Transcribed Image Text:Suppose you make a charge of $1000 to a new credit card, but then charge nothing else and make the minimum payment each month. If the finance charges amount to a monthly rate of 1% and the minimum payment is 6% of the new balance, then your balance B, in dollars, after n payments is an exponential function given by the following formula. B = 1000 x an Here the decay factor a is obtained from the finance charge and the minimum payment as shown in the following formula. a = (1 + 0.01)(1 – 0.06) (a) Find the exact value of the decay factor a. (Round your answer to three decimal places.) (b) By what percentage does your balance decrease each month? (Round your answer to one decimal place.) (c) What will your balance be after you have made payments for 1 years? (Round your answer to two decimal places.) $
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