Question

A 48 gram sample of a substance that’s used for drug research has a k value of 0.1325

Answer 1

Using an exponential function, it is found that the half-life of the substance is of 5.23 units of time.

What is the exponential function for the amount of a substance?

The function is given by:

$A(t) = A(0)e^{-kt}$

In which:

• A(0) is the initial value.

• k is the exponential decay rate.

The parameters are given by:

A(0) = 48,  k = 0.1325.

Hence the equation is:

$A(t) = 48e^{-0.1325t}$

The half-life is the amount of time for which A(t) = 0.5A(0) = 24, hence:

$A(t) = 48e^{-0.1325t}$

$24 = 48e^{-0.1325t}$

$e^{-0.1325t} = 0.5$

$\ln{e^{-0.1325t}} = \ln{0.5}$

$0.1325t = -\ln{0.5}$

$t = -\frac{\ln{0.5}}{0.1325}$

t = 5.23.

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

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