Question

Assuming that the annual rate of inflation averages $4 \%$ over the next 10 years, the approximate costs $C$ of goods or services during any year in that decade can be modeled by $C(t)=P(1.04)^{t},$ where $t$ is the time in years and $P$ is the present cost. The price of an oil change for your car is presently $\$ 29.88 .$ Estimate the price 10 years from now.

Name: Problem 59, Chapter 3: Precalculus
Uploaded: 2021-05-13T19:37:42-08:00
Duration: 1 min 10 s
Channel: Christopher Stanley
Description: Assuming that the annual rate of inflation averages 4 % over the next 10 years, the approximate costs C of goods or services during any year in that decade can be modeled by C(t)=P(1.04)^t, where t is the time in years and P is the present cost. The price of an oil change for your car is presently 29.88 . Estimate the price 10 years from now.

   Assuming that the annual rate of inflation averages $4 \%$ over the next 10 years, the approximate costs $C$ of goods or services during any year in that decade can be modeled by $C(t)=P(1.04)^{t},$ where $t$ is the time in years and $P$ is the present cost. The price of an oil change for your car is presently $\$ 29.88 .$ Estimate the price 10 years from now.

Precalculus

Ron Larson 10th Edition

Chapter 3, Problem 59

Instant Answer

Solved by Expert Christopher Stanley

05/13/2021

Step 1

The present cost of an oil change, $P$, is $29.88. The time, $t$, is 10 years. The annual rate of inflation is $4\%$, which is represented as $1.04$ in the formula. Show more…

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Assuming that the annual rate of inflation averages $4 \%$ over the next 10 years, the approximate costs $C$ of goods or services during any year in that decade can be modeled by $C(t)=P(1.04)^{t},$ where $t$ is the time in years and $P$ is the present cost. The price of an oil change for your car is presently $\$ 29.88 .$ Estimate the price 10 years from now.

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Key Concepts

Exponential Growth

Exponential growth refers to the process of increasing quantity over time at a rate proportional to its current value. This concept is essential in modeling scenarios such as inflation or population growth, where changes compound over time rather than increasing linearly.

Inflation

Inflation is the economic concept that describes the general rise in prices of goods and services over time. It is typically expressed as an annual percentage increase, and understanding inflation is crucial for making future cost predictions and adjustments in both personal finance and economic policy.

Mathematical Modeling

Mathematical modeling involves forming mathematical formulas to represent real-world situations. In this context, exponential functions are used to model how prices or values change over time, allowing predictions about future costs based on current values and growth rates.

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