SOLUTION: The half-time of a radioactive substance is 9 years. If 40 grams of the substance exist initially, how much will remain after 23.5 years? a) 0.077 grams b) 244.30 grams c) 6.11

Question 1190431: The half-time of a radioactive substance is 9 years. If 40 grams of the substance exist initially, how much will remain after 23.5 years?
a) 0.077 grams
b) 244.30 grams
c) 6.11 grams
d) 2.49 grams
e) 6.55 grams
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

Half-life formula
y = a*(0.5)^(x/h)
Alternatively, you can represent the 0.5 as 1/2

a = initial amount
h = half-life, the amount of time it takes to cut in half
x = number of years
y = amount left over after x years pass by

We have the following
a = 40 grams
h = 9 years
x = 23.5 years

So,
y = a*(0.5)^(x/h)
y = 40*(0.5)^(23.5/9)
y = 6.54692287587487 approximately
y = 6.55 grams

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