M2:Average Rate of Change Warmup 2

Find the average rate of change over the given interval. 

• 4

• 7

• 7/3

• 3/7

Answer explanation

To find the average rate of change, use the formula (f(b) - f(a)) / (b - a). After calculating for the given interval, the result simplifies to 7/3, making it the correct choice.

A rocket is 1.5 miles above the Earth in 20 seconds and is 8 miles above the Earth in 2 minutes. What is the rocket's rate of change in miles per second?

• 0.065 mps

• 0.361 mps

• 3.892 mps

• 4.145 mps

Answer explanation

To find the rate of change, calculate the total height change (8 miles - 1.5 miles = 6.5 miles) over the total time (2 minutes = 120 seconds, so 120 seconds - 20 seconds = 100 seconds). Rate = 6.5 miles / 100 seconds = 0.065 mps.

What is the average rate of change from x=0 to x=1

• -3

• 3

• 0

• 2

Answer explanation

The average rate of change is calculated as (f(1) - f(0)) / (1 - 0). If f(1) = 3 and f(0) = 0, then (3 - 0) / (1 - 0) = 3. Thus, the average rate of change from x=0 to x=1 is 3.

The Jamison family kept a log of the distance they traveled during a trip, as represented by the graph below. During which interval was their average speed the greatest?

• the first hour to the second hour

• the second hour to the fourth hour

• the sixth hour to the eighth hour

• the eighth hour to the tenth hour

Answer explanation

The average speed is calculated as distance over time. The first hour to the second hour shows the steepest increase in distance on the graph, indicating the greatest average speed during that interval.

The table below shows the snowfall in a north-eastern city in inches for the first week in January.

Find the average rate of change in the number of inches of snowfall from January 8 to January 11.

• 2/3 in.

• 2 in.

• 3 in.

• 6 in.

Answer explanation

To find the average rate of change from January 8 to January 11, subtract the snowfall on January 8 from that on January 11, then divide by the number of days (3). This gives (2-0)/3 = 2/3 in.

At 0 seconds, Mrs. Taylor was 10 feet off the ground.  At 5 seconds, she was 20 feet off the ground.  What is her rate in feet per second?

• 10 feet per second

• 5 feet per second

• 2 feet per second

• 6 feet per second

Answer explanation

To find the rate, calculate the change in height (20 feet - 10 feet = 10 feet) over the time interval (5 seconds - 0 seconds = 5 seconds). Thus, the rate is 10 feet / 5 seconds = 2 feet per second.