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The average surcharge for non-account holders who use an ATM can be modeled as0.004x3 - 0.061x20.299x + 0.899 dollarsf(x)where x is the number of years since 1998, data between 1998 and 2007.t(a) Write the derivative model for f.f'(x)(b) Estimate the transaction fee in 2012. (Round your answer to two decimal places.)$(c) Estimate the rate of change of the ATM fee in 2008. (Round your answer to three decimal places.)$per year+A

Question
The average surcharge for non-account holders who use an ATM can be modeled as
0.004x3 - 0.061x2
0.299x + 0.899 dollars
f(x)
where x is the number of years since 1998, data between 1998 and 2007.t
(a) Write the derivative model for f.
f'(x)
(b) Estimate the transaction fee in 2012. (Round your answer to two decimal places.)
$
(c) Estimate the rate of change of the ATM fee in 2008. (Round your answer to three decimal places.)
$
per year
+A
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The average surcharge for non-account holders who use an ATM can be modeled as 0.004x3 - 0.061x2 0.299x + 0.899 dollars f(x) where x is the number of years since 1998, data between 1998 and 2007.t (a) Write the derivative model for f. f'(x) (b) Estimate the transaction fee in 2012. (Round your answer to two decimal places.) $ (c) Estimate the rate of change of the ATM fee in 2008. (Round your answer to three decimal places.) $ per year +A

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Step 1

Given the average surcharge is

f(x) 0.004x30.061x2 +0.299x+0.899
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f(x) 0.004x30.061x2 +0.299x+0.899

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Step 2

Differentiate both the sides with respect to x

d
-(0.004x3 - 0.06lx2 +0.299x 0.899)
dx
f(x)
=
f(x) 0.004(3x2)-0.061(2.x)+0.299(1)0
-»f'(x) 0.012x2 - 0.122x+0.299
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d -(0.004x3 - 0.06lx2 +0.299x 0.899) dx f(x) = f(x) 0.004(3x2)-0.061(2.x)+0.299(1)0 -»f'(x) 0.012x2 - 0.122x+0.299

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Step 3

Plug x=14 in f(x) to get the transaction fee in 2012 since the differen...

f(14) 0.00414) -0.06114)2 +0.299(14)+0.899 = 4.105
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f(14) 0.00414) -0.06114)2 +0.299(14)+0.899 = 4.105

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Tagged in

Math

Calculus

Functions

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