Exploring Average Rates of Change in Real-Life Scenarios

A car travels 150 miles in 3 hours. What is the average rate of change in miles per hour?

• 75 miles per hour

• 30 miles per hour

• 50 miles per hour

• 100 miles per hour

A plant grows from 2 inches to 10 inches in 4 weeks. What is the average rate of change in height per week?

• 4 inches per week

• 1 inch per week

• 3 inches per week

• 2 inches per week

A cyclist rides 30 miles in 1.5 hours and then 45 miles in 2 hours. Compare the average rates of change for both segments of the ride.

• The average rate for the first segment is 15 mph, and for the second segment, it is 30 mph. The second segment is slower.

• The average rate for the first segment is 20 mph, and for the second segment, it is 20 mph. Both segments are equal.

• The average rate for the first segment is 25 mph, and for the second segment, it is 20 mph. The first segment is faster.

• The average rate for the first segment is 20 mph, and for the second segment, it is 22.5 mph. The second segment is faster.

A store's sales increased from $2000 to $3000 over 6 months. What is the average rate of change in sales per month?

• 300

• 166.67

• 250

• 100

A runner completes a 5K race in 25 minutes and a 10K race in 55 minutes. What is the average rate of change in speed for each race?

• 1.09 km/h

• 0.75 km/h

• 1.5 km/h

• 2.5 km/h

A student scores 70 on a test and then 85 on the next test after 2 weeks. What is the average rate of change in score per week?

• 5

• 7.5

• 10

• 12.5

A tree grows from 5 feet to 15 feet over 5 years. What is the average rate of change in height per year?

• 2 feet per year

• 3 feet per year

• 1 foot per year

• 4 feet per year

A factory produces 1000 units in the first month and 1500 units in the second month. What is the average rate of change in production per month?

• 1000 units per month

• 300 units per month

• 700 units per month

• 500 units per month

A swimmer completes 100 meters in 50 seconds and 200 meters in 1 minute 40 seconds. Compare the average rates of change for both distances.

• The average rates of change for both distances are equal at 2 meters/second.

• The average rates of change for both distances are different, with 100 meters being faster.

• The average rate of change for the 100 meters is 1 meter/second.

• The average rate of change for the 200 meters is 3 meters/second.

A book's price increases from $15 to $20 over 3 months. What is the average rate of change in price per month?

• $1.25

• $1.50

• $2.00

• $1.67