There was a sample of

600

milligrams of a radioactive substance to start a study. Since then, the sample has decayed by

7.9%

each year.

Let

t

be the number of years since the start of the study. Let

y

be the mass of the sample in milligrams.

Write an exponential function showing the relationship between

y

and

t

Answer: y (t) = 600 (0.921) ^t

Step-by-step explanation:

Given:

Percentage yearly reduction = 7.9%

Initial mass m = 600 mg

time in years = t

An exponential function with yearly decay rate to determine the final mass of the substance is given as:

y (t) = m (f) ^t

y (t) = final mass in milligram

m = 600

f = final mass fraction = 1 - 0.079 = 0.921

f = 0.921

Therefore, the exponential function is given as;

y (t) = 600 (0.921) ^t