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Welcome to our Math lesson on Rate of a Quantity Change, this is the third lesson of our suite of math lessons covering the topic of Rates. Applications of Ratios and Rates in Practice, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.
Earlier we discussed rate examples where time was involved. In such situations, we want to calculate how the other quantity change over time. Therefore, the rates expressing these changes are obtained by dividing two differences: the difference in the given quantity and the difference in time, which in many cases is not evident because we often take the initial time as zero and therefore, the difference in time simply gives the final time.
In general, we have Y for the rate of a quantity change:
The price of an item in 2019 was $80 and in 2024 the same item was priced at $120. What is the yearly (annual) rate of the price increase?
Here, the quantity Y represents the price. Thus, using the general formula of rate of change
we obtain
The rate of a quantity change can be also negative. This means the final value of the quantity involved is smaller than the initial value because the quantity decreases. Look at the example below.
The price of petrol during lockdown caused by the COVID-19 pandemic dropped uniformly from $2.15/gallon to $1.73/gallon in two weeks due to the reduced use of cars. What was the rate of price change during this period?
Price reduction here represents the rate of price change. We have
Here, Y represents the price and tfinal - tinitial = 2 weeks = 14 days. Hence,
This result means the price dropped by a rate of $0.03 per day.
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