Average Rate of Change Word Problem Help?

In summary, the concept of average rate of change is a measure of how quickly a quantity changes over a specific interval of time. To solve word problems involving average rate of change, one must identify the changing quantities and time interval, use the formula to calculate the rate, and interpret the result in context. Average rate of change can be negative, indicating a decrease in quantity over time. It has various real-life applications in fields such as economics, physics, and biology. To check the accuracy of an answer to an average rate of change word problem, one can plug in the given values and compare the result to the calculated rate, or use logic and reasoning to determine if the answer makes sense in the given context.
  • #1
madeeeeee
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Average Rate of Change Word Problem Help!?

12. A ball is thrown vertically upward from a roof of a school that is 20 m high. The equation which gives its height above ground, in metres, after t seconds, is h(t) = - 4.9t2 + 3t + 20,
a) Calculate the average rate of change of the ball between 1 and 4 seconds. [2 marks]

answer:
h(4)-h(1) / 3

-3.6 m/s

is this right?


b) Determine the instantaneous rate of change when t = 1 s. [4 marks]

answer:
h(t) = - 4.9t2 + 3t + 20
h'(t)= -9.8t + 3
= -9.8(1) + 3
= -6.8 m/s
At t= 1s, the skydiver is falling at a rate of -6.8 m/s.

is this right?
 
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  • #2


madeeeeee said:
12. A ball is thrown vertically upward from a roof of a school that is 20 m high. The equation which gives its height above ground, in metres, after t seconds, is h(t) = - 4.9t2 + 3t + 20,
a) Calculate the average rate of change of the ball between 1 and 4 seconds. [2 marks]

answer:
h(4)-h(1) / 3

-3.6 m/s

is this right?
No, it is not. What did you get for h(4) and h(1)?




b) Determine the instantaneous rate of change when t = 1 s. [4 marks]

answer:
h(t) = - 4.9t2 + 3t + 20
h'(t)= -9.8t + 3
= -9.8(1) + 3
= -6.8 m/s
At t= 1s, the skydiver is falling at a rate of -6.8 m/s.

is this right?
Yes, that is correct.
 

FAQ: Average Rate of Change Word Problem Help?

What is the concept of average rate of change?

The average rate of change is a measure of how quickly a quantity changes over a specific interval of time. It is calculated by dividing the change in the quantity by the change in time.

How do I solve word problems involving average rate of change?

To solve word problems involving average rate of change, you first need to identify the quantities that are changing and the time interval over which they are changing. Then, use the formula for average rate of change to calculate the rate. Finally, interpret the result in the context of the problem.

Can average rate of change be negative?

Yes, average rate of change can be negative. This means that the quantity is decreasing over time, or that there is a negative change in the quantity over the given time interval.

What are some real-life applications of average rate of change?

Average rate of change is used in many fields, such as economics, physics, and biology. It can be used to calculate the speed of an object, the rate of population growth, or the change in stock prices over time.

How can I check if my answer to an average rate of change word problem is correct?

You can check your answer by plugging the given values into the formula for average rate of change and comparing the result to your calculated rate. You can also use logic and reasoning to determine if your answer makes sense in the context of the problem.

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