Question

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 1

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