Question

The amount of a radioactive substance remaining after t years is given by the function f(t) = m(0.5)", where m is the
initial mass and h is the half-life in years. Cobalt-60 has a half-life of about 5.3 years. Which equation gives the
mass of a 50 mg Cobalt-60 sample remaining after 10 years, and approximately how many milligrams remain?

Answer 1

Using an exponential function, it is found that the equation is:

$f(1.8868) = 60(0.5)^{1.8868}$

Which means that approximately 16.22 mg remain.

What is an exponential function?

A decaying exponential function is modeled by:

$A(t) = A(0)(1 - r)^t$

In which:

• A(0) is the initial value.

• r is the decay rate, as a decimal.

In this problem, the equation is:

$f(h) = m(0.5)^h$

We work with a 50 mg Cobalt-60 sample, hence m = 60, and considering a half-life of 5.3 years, in 10 years we have h = 10/5.3 = 1.8868. Hence the equation is:

$f(1.8868) = 60(0.5)^{1.8868} = 16.22$

Approximately 16.22 mg remain.

More can be learned about exponential functions at https://brainly.com/question/25537936