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Welcome to our Math lesson on Finding the Inverse Formula, this is the sixth lesson of our suite of math lessons covering the topic of Writing Formulas and Substituting in a Formula, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.
Sometimes, the independent variable in a formula is known and the value of one of dependent variables is required. In this case, we need to find a new formula based on the original one but which expresses the new unknown quantity in terms of the known ones. This is known as the inverse formula. For example, in the formula
we may have the y known and berequired to calculate x. In this case, we isolate x (as unknown) and write the rest of formula in terms of y. Thus, we have
For example, if y = 7 and we need to find x, we obtain
The number N of dust particles per cubic centimetre present in the environment at an industrial site in terms of the raining time t (in minutes) is given by the formula
Calculate the raining time necessary to reduce the air pollution to 8 particles per cubic centimetre.
We already know N but we need to calculate the time t. Thus, we isolate t to express it in terms of N. We have
Given that N = 8, we obtain
Hence, if it rains ceaselessly for 100 minutes in the given site, the air pollution reduces to 8 particles per cubic centimetre.
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