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Chapter 6: Problem 5

The U.S. Census Bureau reports that from the 2000 U.S. Census to July 2008 , the population of the state of Arizona increased by approximately \(26.7 \% .\) The population in 2008 was \(6,500,180\). What was Arizona's population in the 2000 census?

Short Answer

Expert verified
Answer: The approximate population of Arizona in the 2000 census was 5,130,609.

Step by step solution

01

Convert the percentage to a decimal

To work with the increase, we need to convert the \(26.7 \%\) increase to a decimal. Divide by \(100\) to do this: \(26.7 \% = \frac{26.7}{100} = 0.267\)
02

Calculate the total increase in population

The population increased by \(0.267\) times the original population. Let \(x\) be the population in 2000, then the increase in population can be represented as \(0.267x\).
03

Find the population in 2000

We know that the population in 2008 is \(6,500,180\). Now, we need to subtract the increase in population from the 2008 population to find the population in 2000. We can do this with the equation: \(x + 0.267x = 6,500,180\)
04

Solve for x

To find the value of \(x\), we first combine the terms with \(x\): \((1 + 0.267)x = 6,500,180\) \(1.267x = 6,500,180\) Now, divide both sides by \(1.267\) to isolate \(x\): \(x = \frac{6,500,180}{1.267}\)
05

Calculate the population in 2000

Now we can find the value of \(x\): \(x = 5,130,608.654\) Since the population must be a whole number, we can round it to the nearest integer: \(x \approx 5,130,609\) So, Arizona's population in the 2000 census was approximately \(5,130,609\).

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