The number of crimes that occurred in a certain city per 1000 people had decreased from 

46.946.9 

in 1920 to 

46.246.2 

in 

19551955. 

Find the average rate of change in the number of crimes per 1000 people that occurred from 1920 to 

19551955.

To find the average rate of change in the number of crimes per 1000 people from 1920 to 1955, we can use the formula for the average rate of change:

\[
\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}
\]

Where:
- \( f(a) \) is the number of crimes in 1920, \( f(b) \) is the number of crimes in 1955,
- \( a \) is the year 1920, and \( b \) is the year 1955.

From the given values:
- \( f(1920) = 46.9 \),
- \( f(1955) = 46.2 \),
- \( a = 1920 \),
- \( b = 1955 \).

Now, we apply these values to the formula:

\[
\text{Average Rate of Change} = \frac{46.2 - 46.9}{1955 - 1920}
\]

\[
\text{Average Rate of Change} = \frac{-0.7}{35} = -0.02
\]

Thus, the average rate of change is:

\[
-0.02 \, \text{crimes per 1000 people per year}.
\]

This means that, on average, the number of crimes per 1000 people decreased by 0.02 per year between 1920 and 1955.

Would you like further details or have any questions?

Here are 5 related questions:
1. How do you interpret the negative rate of change in real-world terms?
2. Can you apply the same method to other time intervals, say 1955 to a later year?
3. How would you model the change in crime rate if the pattern continued beyond 1955?
4. What factors could contribute to a change in crime rates over a period of time?
5. Could other factors besides time affect the rate of change in crime statistics?

**Tip**: Average rate of change is essentially the slope of the line connecting two points on a graph—useful for comparing how a value changes over time.

The number of crimes that occurred in a certain city per 1000 people had decreased from 46.9 in 1920 to 46.2 in 1955. Find the average rate of change in the number of crimes per 1000 people that occurred from 1920 to 1955.

Find the average rate of change in the crime rate per 1000 people in a city from 1920 to 1955. This problem involves algebraic concepts such as the rate of change and slope, suitable for students in Grades 9-12.

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