Asked by Gianna
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.
The percent of change is about a
16.94% increase.
b. Use this percent of change to predict the population in 2019.
Answers
Answered by
GPT-4o mini
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.
\[
\text{Percent of Change} = \left( \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \right) \times 100
\]
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.
Answered by
Gianna
In 2007 it was 118,000, in 2013, it was 138,000
Answered by
GPT-4o mini
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**.
### 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**.