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In this lesson, we will learn how to find the rate of change using tables and graphs and solve real-world problems using rate of change.

Q1:

What is the rate of change for the function shown in the given graph?

Q2:

What is the rate of change shown by this graph of a function?

Q3:

What is the average speed of a sound wave that travels 895 metres in 2.5 seconds?

Q4:

What is the initial value and the rate of change for the function represented by the given table?

Q5:

The graph below shows the relation between the cost of a party and the number of people attending. Determine the rate of change.

Q6:

Adam opened a savings account with $145. Every month, he made the same deposit and made no withdrawals. After 3 months, he had $214. After 6 months, he had $352. After 9 months, he had $559. Determine the rate of change in his savings account.

Q7:

At 5:00, the water level in a pool reaches a height of 10 inches. At 8:00, the water level is at 50 inches. What is the rate of change of the water level per minute?

Q8:

What is the rate of change for the function represented in the following table?

Q9:

What is the initial value and the rate of change for the function represented by the given graph?

Q10:

This graph illustrates the decay of a radioactive substance over π‘ days. Which of the following is the best estimate of the average decay rate from π‘ = 5 to π‘ = 1 5 ?

Q11:

If a worker who can paint a house in 300 hours and another who can paint the same house in 100 hours work together, how many minutes do they need to paint the house?

Q12:

A cityβs population in the year 1960 was 2 8 7 5 0 0 and 2 7 5 9 0 0 in 1989. Find the average rate of the population growth, in terms of people per year, and explain what it tells us about how the population changes each year.

Q13:

The following graph is a plot of the height in meters of a kite over a 4-minute period.

What was the greatest speed, in meters per minute, at which the kite was moving? Was it descending or ascending?

Q14:

A sphere of mass 2.4 kg was moving through a dusty atmosphere. The dust accumulated on its surface at a rate of 125 g/min. How long will it take until the sphereβs mass becomes 4 kg?

Q15:

Tap A takes 240 minutes to fill an aquarium. Tap B takes 80 minutes to fill the same aquarium. Tap C only takes 20 minutes to fill the aquarium. If all three taps were used together, how many seconds would it take to fill the aquarium?

Q16:

A worker painted a wall with an area of 42 m^{2} in 3 hours. What is his average work rate in m^{2}/h, and how many square metres of wall would he be able to paint at that rate in 2 hours?

Q17:

If Farida mows her yard in 2 hours and her sister Dina can mow the yard in 3 hours, then how long will it take them working together to mow the yard?

Q18:

Consider the function β = { ( 0 , 4 ) , ( 1 , 1 ) , ( 2 , 3 ) , ( 3 , 2 ) , ( 4 , 3 ) } .

Over which interval does the average rate of change of β have greatest magnitude?

Over which interval is the average rate of change of β least?

Q19:

Over which interval is the average rate of change of β greatest?

Q20:

A phone company charges for service according to the formula: πΆ ( π ) = 2 4 + 0 . 1 π , where π is the number of minutes used and πΆ ( π ) is the monthly charge in dollars. Find and interpret the rate of change and the initial value.

Q21:

As a raindrop was falling, water vapour condensed on its surface increasing its mass at a rate of 4 milligrams per second. Given that at a certain moment its mass was 0.9 g, find its mass 2 minutes later.

Q22:

Shady is depositing money into a bank account. After 3 months, there is $147 in the account, and after 7 months, there is $343 in the account. Find the rate of change of the account.

Q23:

Determine the average rate of change of the function π ( π₯ ) = 9 π₯ + 7 2 when π₯ = π₯ 1 .

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