Question

What is the percent rate??

Answer 1

Using an exponential function, it is found that the decay rate is of 6.24% a year.

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.

The half-life is of 10.75 years, hence A(10.75) = 0.5A(0) and this is used to find the decay rate r.

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

$0.5A(0) = A(0)(1 - r)^{10.75}$

$(1 - r)^{10.75} = 0.5$

$\sqrt[10.75]{(1 - r)^{10.75}} = \sqrt[10.75]{0.5}$

$1 - r = (0.5)^{\frac{1}{10.75}}$

1 - r = 0.9376.

r = 1 - 0.9376.

r = 0.0624.

The decay rate is of 6.24% a year.

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

#SPJ1