Question

In the following exercises, use an exponential model to solve. In the last ten years the population of Indonesia has grown at a rate of $1.12 \%$ per year to 258,316,051 . If this rate continues, what will be the population in 10 more years?

Name: Problem 121, Chapter 10: Intermediate Algebra
Uploaded: 2022-09-30T16:51:44-08:00
Channel: Nicole Hoffman
Description: In the following exercises, use an exponential model to solve. In the last ten years the population of Indonesia has grown at a rate of 1.12 % per year to 258,316,051 . If this rate continues, what will be the population in 10 more years?

   In the following exercises, use an exponential model to solve.
In the last ten years the population of Indonesia has grown at a rate of $1.12 \%$ per year to 258,316,051 . If this rate continues, what will be the population in 10 more years?

Intermediate Algebra

Lynn Marecek 2nd Edition

Chapter 10, Problem 121

Instant Answer

Solved by Expert Nicole Hoffman

09/30/2022

Step 1

The exponential model is given by the formula: \[ P = P_0 * (1 + r)^t \] where: - $P$ is the future value of the population. - $P_0$ is the present value of the population. - $r$ is the growth rate (expressed as a decimal). - $t$ is the time in years. Show more…

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In the following exercises, use an exponential model to solve. In the last ten years the population of Indonesia has grown at a rate of $1.12 \%$ per year to 258,316,051 . If this rate continues, what will be the population in 10 more years?

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Key Concepts

Growth Rate

The growth rate is the percentage change per time period that quantifies how quickly a quantity increases or decreases. In the context of exponential models, it is used to determine the factor by which a population or investment multiplies over time.

Exponential Model

An exponential model is a mathematical representation that describes processes that increase or decrease at rates proportional to their current values. It is often expressed with the formula P = P?(1 + r)^t, where P? is the initial amount, r is the rate, and t is time, and is widely used for projecting future population sizes, investments, and other phenomena.

Exponential Growth

Exponential growth refers to an increase that occurs at a rate proportional to the current size, meaning that as the population grows, the amount added in each time period increases. This concept is critical in many fields such as biology and finance where systems grow multiplicatively instead of additively.

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