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sashaice [31]
3 years ago
15

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 n

umber of milligrams of the substance and t represents the time. In years. In the function p(t), explain what 0.25 and 500 represent.​
Mathematics
1 answer:
ludmilkaskok [199]3 years ago
3 0

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.

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