Question

In 2001 , a sample of a radioactive substance had a mass of 800 milligrams. Since then, the sample has decayed by 7.2 % each year. Let t be the number of years since 2001 . Let y be the mass of the substance in milligrams. Write an exponential function showing the relationship between y and t

Answer 1

Explanation:

We need to write our function in the formula for Exponential Decay a(1-r)^x

We can represent "a" in our equation as the original sample size for the substance (800 mg).

According to the formula, we need to subtract our rate of decay from 1. Remember! We CANNOT use the percent's decimal as a number. We need to convert the percent to a decimal. We do this by moving the decimal place backwards 2 places. 7.2% = .072

1 - .072 = .28

Now we have the equation f(x) = 800(0.28). But where are the variables? That is our next problem. If t is the number of years since 2001, then we need to multiply it by the rate of decay (.28t). Now there is only one variable left, which is y.
Our answer is f(x) = 800(.28t)^y