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.​

Answer 1

Given:

The function is:

`p(t)=500(0.25)^t`

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:

`y=ab^x` ...(i)

Where, a is the initial value and b is the growth/decay factor. If
`0<b<1`, then decay factor and if
`b>1`, then growth factor.

We have,

`p(t)=500(0.25)^t` ...(ii)

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

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

`b=0.25`, 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.