If the annual rate of inflation averages 4% over the next 10 years,the approximate cost C of goods or services during any year in that decade is where t is the time in years and P is the present cost.The price of an oil change for your car is presently $24.75.Find the rate of change of C with respect to t when .Round your answer to three decimal places.
A)38.101 dollars per year
B)1.010 dollars per year
C)1.437 dollars per year
D)10.644 dollars per year
E)84.358 dollars per year

Question

If the annual rate of inflation averages 4% over the next 10 years,the approximate cost C of goods or services during any year in that decade is  where t is the time in years and P is the present cost.The price of an oil change for your car is presently $24.75.Find the rate of change of C with respect to t when  .Round your answer to three decimal places. ​
A)38.101 dollars per year 
B)1.010 dollars per year 
C)1.437 dollars per year 
D)10.644 dollars per year 
E)84.358 dollars per year

Quizplus · Accepted Answer

First, we need to plug in the given values into the equation to find C when t = 11.

C = P(1 + r)^t
C = $24.75(1 + 0.04)^11
C = $39.42

Next, we need to find the derivative of C with respect to t.

dC/dt = P(ln(1 + r))(1 + r)^t

Plugging in the values we get 
dC/dt = $24.75(ln(1.04))(1.04)^11
dC/dt = $1.437

Therefore, the rate of change of C with respect to t is $1.437 per year.

If the Annual Rate of Inflation Averages 4% Over the Next