Rate Of Change Practice Formative Assessment

1. The population of a city rises from 100,000 to 226,000 over a ten-year period. Find the average rate of change in people per year.

0.000079 people per year

12,600 people per year

0.4375 people per year

2.29 people per year

The average rate of change in people per year can be found by taking the difference in population and dividing it by the number of years. In this case, the population increased by 126,000 (226,000 - 100,000) over a ten-year period. Dividing this by 10 (the number of years) gives us an average rate of change of 12,600 people per year.

Explanation

The average rate of change in people per year can be found by taking the difference in population and dividing it by the number of years. In this case, the population increased by 126,000 (226,000 - 100,000) over a ten-year period. Dividing this by 10 (the number of years) gives us an average rate of change of 12,600 people per year.

2. Which statement about rate of change is true?

It measures the increase or decrease of a function.

It measures change over time

The statement "It measures change over time" is true because the rate of change is a concept used to quantify how a quantity or variable changes with respect to another variable, typically over a specific period of time. It allows us to determine the speed or slope at which a function is changing over a given interval or time period. Therefore, it provides information about the rate or speed of change over time.

Explanation

The statement "It measures change over time" is true because the rate of change is a concept used to quantify how a quantity or variable changes with respect to another variable, typically over a specific period of time. It allows us to determine the speed or slope at which a function is changing over a given interval or time period. Therefore, it provides information about the rate or speed of change over time.

3. In the Mojave Desert in California, temperatures can drop quickly from day to night. Suppose the temperature drops from 100 degrees at 2 P.M. to 68 degrees at 5 A.M. Find the average rate of change of degrees per hour.

3 degrees per hour

-3 degrees per hour

-2 degrees per hour

2 degrees per hour

The average rate of change of degrees per hour is calculated by finding the difference in temperature and dividing it by the time interval. In this case, the temperature dropped from 100 degrees to 68 degrees over a time period of 15 hours (from 2 P.M. to 5 A.M.). The difference in temperature is 100 - 68 = 32 degrees. Dividing this by the time interval gives us 32/15 = 2.13 degrees per hour. Rounding to the nearest whole number, the average rate of change is -2 degrees per hour.

Explanation

The average rate of change of degrees per hour is calculated by finding the difference in temperature and dividing it by the time interval. In this case, the temperature dropped from 100 degrees to 68 degrees over a time period of 15 hours (from 2 P.M. to 5 A.M.). The difference in temperature is 100 - 68 = 32 degrees. Dividing this by the time interval gives us 32/15 = 2.13 degrees per hour. Rounding to the nearest whole number, the average rate of change is -2 degrees per hour.

4. You are driving through Europe. At 9:00 A.M. you are 420 kilometers from Rome. At 3:00 P.M. you are 108 kilometers from Rome. Find your average speed.

35 mph

40 mph

45 mph

50 mph

To find the average speed, we need to calculate the total distance traveled and the total time taken. From 9:00 A.M. to 3:00 P.M., a total of 6 hours have passed. The distance covered during this time is 420 - 108 = 312 kilometers. Therefore, the average speed is 312 km / 6 hours = 52 km/h. However, the answer choices are in mph, so we need to convert km/h to mph. 52 km/h is approximately 32.31 mph, which is closest to 35 mph. Therefore, the correct answer is 35 mph.

Explanation

To find the average speed, we need to calculate the total distance traveled and the total time taken. From 9:00 A.M. to 3:00 P.M., a total of 6 hours have passed. The distance covered during this time is 420 - 108 = 312 kilometers. Therefore, the average speed is 312 km / 6 hours = 52 km/h. However, the answer choices are in mph, so we need to convert km/h to mph. 52 km/h is approximately 32.31 mph, which is closest to 35 mph. Therefore, the correct answer is 35 mph.