## 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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2 weeks 2021-09-05T14:21:43+00:00 1 Answers 0 views 0

1. 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.