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Suppose that the growth of a population (in thousands) is represented by the expression 32(2.1)^x...

Question:

Suppose that the growth of a population (in thousands) is represented by the expression {eq}32(2.1)^x {/eq} where x represents the number of years since 2010. Evaluate the expression for the year 2015. Round to the nearest whole number.

Evaluating Expressions


Evaluating expressions for a certain value means finding the value of the expression when the unknown variable takes a certain value. In the question given, the important thing to note is that the x is the number of years after 2010.

Answer and Explanation:


In the expression that gives the population (in thousands), x is the number of years since 2010. We want to evaluate the expression for the year 2015. The year 2015 is 5 years after 2010. This means that x takes the value 5 so that x=5.

To now find the population in 2015, we substitute the value of x with 5 in the expression.

$$\begin{align} \text{Population (in thousands)}&=32(2.1)^5\\ &=1306.912\\ \therefore \text{Population in 2015}&=1306.912*1000\\ &=1,306,912 \end{align} $$


Learn more about this topic:

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Evaluating Simple Algebraic Expressions

from ELM: CSU Math Study Guide

Chapter 6 / Lesson 3
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