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## The breakdown of a sample of a chemical compound is represented by the function p(t) = 500 (0.25)^t, where p(t) represents the number of mil

Question

The breakdown of a sample of a chemical compound is represented by the function p(t) = 500 (0.25)^t, where p(t) represents the number of milligrams of the substance and t represents the time. In years. In the function p(t), explain what 0.25 and 500 represent.

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Mathematics
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2021-09-05T14:21:43+00:00
2021-09-05T14:21:43+00:00 1 Answers
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## Answers ( )

Given:The function is:

Where p(t) represents the number of milligrams of the substance and t represents the time.

To find:The correct explanation for the number 0.25 and 500 in the given function.

Solution:The general exponential function is:

…(i)

Where, a is the initial value and b is the growth/decay factor. If , then decay factor and if , then growth factor.

We have,

…(ii)

On comparing (i) and (ii), we get

, it means initial there are 500 milligrams of the substance.

, this value is less than 1, it means the substance is decreasing by a factor of 0.25.

Therefore, 0.25 means the substance is decreasing by a factor of 0.25 and 500 means the initial value of substance is 500 milligram.