Question

The half-life of a certain radioactive material is 37 days. An initial amount of the material has
a mass of 477 kg. Write an exponential function that models the decay of this material. Find
how much radioactive material remains after 6 days. Round your answer to the nearest
thousandth.

Answer 1

Answer is option B that ends with 426.288 kg.

Answer 2

The exponential function that models the decay of this material is $477(\frac{1}{2})^{(\frac{t}{37} )}$ and the quantity of substance remains is 426.28 grams

What is Half life?

Half-life, in radioactivity, the interval of time required for one-half of the atomic nuclei of a radioactive sample to decay.

What is Radioactive material?

Radionuclides (or radioactive materials) are a class of chemicals where the nucleus of the atom is unstable

Given,

Half life of a certain radioactive material = 37 days

Initial amount of the material = 477 grams

Quantity of substance remains N(t) = $N_{0}(\frac{1}{2})^{(\frac{t}{half-life} )}$

Substitute the value in the equation N(t) =$477(\frac{1}{2})^{(\frac{t}{37} )}$

$477(\frac{1}{2})^{(\frac{t}{37} )}$ is the exponential function that models the decay of this material.

Quantity of substance remains after 6 days = $477(\frac{1}{2})^{(\frac{6}{37} )}$ = 426.28 grams

Hence, the exponential function that models the decay of this material is $477(\frac{1}{2})^{(\frac{t}{37} )}$ and Quantity of substance remains is 426.28 grams  

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