3. the half-life of a certain radioactive material is 42 days. an initial amount of the material has a mass of 49
kg. write an exponential function that models the decay of this material. find how much radioactive material
remains after 8 days. round your answer to the nearest thousandth

Answer;

= 42.940 kg

Explanation;

Half-life = 42 days

Initial amount = 49 kg

Therefore,

New mass = original mass × (1/2)^n; where n is the number of half lives.

n = 8/42

New mass =  49 × (1/2)^(8/42)

                  = 49 × 2^(-8/42)

                  = 42.9395

                  = 42.940 kg (to the nearest thousandth)

The exponential function will be;

An exponential function that models a radioactive decay would be written as:

An = Ao e^-kt

where An is the amount of the material left after a certain time, t. Ao is the initial amount. k is a constant. 

We use the value of the half-life to find the value of k.

1/2Ao = Ao e^-k(42 days)
k = 0.0165 

The amount remaining after 8 days is calculated as follows:

An = 49 e^(-0.0165)(8)
An = 42.9407 kg

The answer is orbit around nucleus