Question

1. mp modeling real life the table shows population data for a community.

a. what is the percent of change from 2011 to 2017?
b. predict the population in 2023. explain your reasoning.

year	population
2017	138,000

Explanation:

Part (a)

Step1: Recall percent change formula

The formula for percent change is $\text{Percent Change} = \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \times 100\%$. Here, the old value (2011 population) is 118,000 and the new value (2017 population) is 138,000.

Step2: Calculate the difference

First, find the difference: $138000 - 118000 = 20000$.

Step3: Apply the formula

Now, substitute into the formula: $\frac{20000}{118000} \times 100\% \approx 16.95\%$.

Part (b)

Step1: Determine the time interval and growth per interval

From 2011 to 2017 is 6 years, and the population grew by 20,000 (as calculated in part a). So the average annual growth is $\frac{20000}{6} \approx 3333.33$ per year.

Step2: Predict 2023 population

From 2017 to 2023 is another 6 years. So we add the growth over 6 years to the 2017 population. The growth is $3333.33 \times 6 \approx 20000$. So the predicted population in 2023 is $138000 + 20000 = 158000$ (assuming linear growth, as we used the average annual growth from the previous 6 - year period).

Answer:

s:
a. The percent of change is approximately $\boxed{17.0\%}$ (rounded to one decimal place) or about $16.95\%$.
b. The predicted population in 2023 is $\boxed{158000}$ (assuming linear growth; other growth models could give different results).