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

The percent of change is about a
16.94% increase.

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

3 answers

To calculate the percent of change from 2007 to 2013, you typically use the formula:

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

If the percent of change from 2007 to 2013 is given as approximately 16.94%, we can use that to predict the population in 2019.

To predict the population in 2019, we can apply the same percent increase (16.94%) assuming the population continues to grow at the same rate.

Assuming the population in 2013 (let's call it \( P_{2013} \)) can be represented as:

\[ P_{2013} = P_{2007} \times (1 + 0.1694) \]

The population for 2019 can similarly be predicted, assuming another 16.94% increase:

\[ P_{2019} = P_{2013} \times (1 + 0.1694) = P_{2007} \times (1 + 0.1694)^2 \]

Now, let’s denote \( P_{2007} \) as the initial population in 2007. This gives:

\[ P_{2019} = P_{2007} \times (1.1694)^2 \]

Calculating \( (1.1694)^2 \):

\[ (1.1694)^2 \approx 1.37267 \]

Therefore, the predicted population in 2019 would be:

\[ P_{2019} \approx P_{2007} \times 1.37267 \]

To finalize the prediction, you need the population of a specific year (2007) to calculate \( P_{2019} \). If you provide that value, I can help complete the calculation for predicting the population in 2019.

In 2007 it was 118,000, in 2013, it was 138,000

Given the population in 2007 was 118,000 and in 2013 it was 138,000, we can affirm the percent change calculation to ensure accuracy.

Step 1: Calculate the Percent of Change

Using the formula:

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

Substituting the values:

\[ \text{Percent of Change} = \left( \frac{138,000 - 118,000}{118,000} \right) \times 100 \] \[ = \left( \frac{20,000}{118,000} \right) \times 100 \approx 16.95% \]

This confirms the provided percent change of approximately 16.94% is accurate (rounded).

Step 2: Predict the Population in 2019

Now, we'll use the percent change to predict the population in 2019.

Calculation of Population in 2019

Using the same percent increase for another cycle (applying the increase again):

\[ P_{2019} = P_{2013} \times (1 + 0.1694) \]

Substituting \( P_{2013} = 138,000 \):

\[ P_{2019} = 138,000 \times 1.1694 \approx 161,000.20 \]

Rounding to the nearest whole number, the predicted population in 2019 is:

\[ P_{2019} \approx 161,000 \]

Conclusion

Based on the calculated percent of change and the population data provided, the predicted population in 2019 would be approximately 161,000.