Question

If the decay of 742 mg of an isotope is described by the function A(t)= 742e-0.03t, where t is time in years. Find the amount left after 84 years. Round your answer to the nearest mg.

Answer 1

57.701 mg before rounding

Answer 2

The amount left after 84 years is 59.70 mg.

Explanation:

Given : If the decay of 742 mg of an isotope is described by the function
`A(t)= 742e^(-0.03t)`, where t is time in years.

To find : The amount left after 84 years?

Solution :

The function of decay of 742 mg of an isotope is given by,

`A(t)= 742e^(-0.03t)`

We have to find the amount left after 84 years.

i.e. put t=84 in the given function,

`A(84)= 742e^(-0.03* 84)`

`A(84)= 742e^(-2.52)`

`A(84)= 59.701`

Therefore, The amount left after 84 years is 59.70 mg.