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.