Question

The half-life of radium-226 is 1600 years. Suppose we have a 27-mg sample.

Answer 1

A function m(t)= m₀e^(-rt) that models the mass remaining after t years is; m(t) = 27e^(-0.00043t)

The amount of sample that will remain after 4000 years is; 4.8357 mg

The number of years that it will take for only 17 mg of the sample to remain is;  1076 years

How to solve exponential decay function?

A) Using the model for radioactive decay;

m(t)= m₀e^(-rt)

where;

m₀ is initial mass

r is rate of growth

t is time

Thus, we are given;

m₀ = 27 mg

r = (In 2)/1600 = -0.00043 which shows a decrease by 0.00043

and so we have;

m(t) = 27e^(-0.00043t)

c) The amount that will remain after 4000 years is;

m(4000) = 27e^(-0.00043 * 4000)

m(4000) = 27 * 0.1791

m(4000) = 4.8357 mg

d) For 17 mg to remain;

17 = 27e^(-0.00043 * t)

17/27 = e^(-0.00043 * t)

In(17/27) = -0.00043 * t

-0.4626/-0.00043 = t

t = 1076 years

Read more about Exponential decay function at; brainly.com/question/27822382

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