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 $0$, 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.