Question

Cobalt-60 is subject to radioactive decay, and each year the amount present is reduced by 12.3%. (a) The amount of cobalt-60 present is an exponential function of time in years. What is the base of this exponential function? . (b) What is the half-life of cobalt-60? Round your answer to one decimal place. yr

Answer 1

Using an exponential function, it is found that:

a) The base is of 0.877.

b) The half-life of cobalt-60 is of 5.3 years.

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, and 1 - r is the base.

Item a:

Each year the amount present is reduced by 12.3%, hence $r = 0.123$, and the base is:

$1 - r = 1 - 0.123 = 0.877$

Item b:

This is t for which A(t) = 0.5A(0), hence:

$A(t) = A(0)(0.877)^t$

$0.5A(0) = A(0)(0.877)^t$

$(0.877)^t = 0.5$

$\log{(0.877)^t} = \log{0.5}$

$t\log{0.877} = \log{0.5}$

$t = \frac{\log{0.5}}{\log{0.877}}$

$t = 5.3$

The half-life of cobalt-60 is of 5.3 years.

You can learn more about exponential functions at https://brainly.com/question/25537936