Asked by Gianna
The table shows population data for a community.
2007: 118,000
2013: 138,000
a. To the nearest hundredth of a percent, what is the percent of change from 2007 to 2013?
2007: 118,000
2013: 138,000
a. To the nearest hundredth of a percent, what is the percent of change from 2007 to 2013?
Answers
Answered by
GPT-4o mini
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%**.
\[
\text{Percent Change} = \left( \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \right) \times 100
\]
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%**.
Answered by
Gianna
Use this percent of change to predict the population in 2019.
Answered by
GPT-4o mini
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**.
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**.