The table shows population data for a community.

Question

2007: 118,000
2013: 138,000

a. To the nearest hundredth of a percent, what is the percent of change from 2007 to 2013?

Answer 1

To calculate the percent change from 2007 to 2013, you can use the formula for percent change:

\[ \text{Percent Change} = \left( \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \right) \times 100 \]

In this case:

• Old Value (2007 population) = 118,000
• New Value (2013 population) = 138,000

Now, plug in the values:

\[ \text{Percent Change} = \left( \frac{138,000 - 118,000}{118,000} \right) \times 100 \]

Calculate the difference:

\[ 138,000 - 118,000 = 20,000 \]

Now, substitute this back into the formula:

\[ \text{Percent Change} = \left( \frac{20,000}{118,000} \right) \times 100 \]

Now perform the division:

\[ \frac{20,000}{118,000} \approx 0.169491 \]

Now multiply by 100:

\[ 0.169491 \times 100 \approx 16.9491 \]

Finally, rounding to the nearest hundredth of a percent:

\[ \text{Percent Change} \approx 16.95% \]

Thus, the percent change from 2007 to 2013 is approximately 16.95%.

Answer 2

Use this percent of change to predict the population in 2019.

Answer 3

To predict the population in 2019 using the percent of change calculated earlier (16.95% over a 6-year span), we first need to calculate the population change over each 6-year period.

1. Calculate the growth rate:

   • The population from 2007 to 2013 increased by 16.95%, which we can use to estimate the change in the next 6 years (2013 to 2019).

2. Apply the growth rate to the 2013 population:

   • The population in 2013 was 138,000.

The formula for calculating the new population based on the growth rate is:

\[ \text{New Population} = \text{Old Population} \times (1 + \text{Growth Rate}) \]

Convert the percentage to a decimal for the calculation:

\[ \text{Growth Rate} = \frac{16.95}{100} = 0.1695 \]

Now, apply this growth rate:

\[ \text{Predicted Population in 2019} = 138,000 \times (1 + 0.1695) \]

\[ = 138,000 \times 1.1695 \]

Calculating this:

\[ = 161,751 \]

Therefore, the predicted population in 2019 is approximately 161,751.