Problema Solution

there was a sample of 900 milligrams of a radioactive substance to start a study. since the sample has decayed by 9.5% 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 provided by our tutors

There was a sample of 900 milligrams of a radioactive substance to start a study. In terms of y and t this means:

t = 0 years

y = 900

After t = 1 year 9.5% will decay and what is left is:

y = 900(1 - 0.095)

After t = 2 years another 9.5% will decay and there will be:

y = 900(1 - 0.095)(1 - 0.095)

y = 900(1 - 0.095)^2

After t = 3 years another 9.5% will decay and there will be:

y = 900(1 - 0.095)^2 (1 - 0.095)

y = 900(1 - 0.095)^3

After t years there will be:

y = 900(1 - 0.095)^t  or y = 900*0.905^t milligrams of radioactive substance left.