Element X is a radioactive isotope such that every 38 years, its mass decreases by

half. Given that the initial mass of a sample of Element X is 890 grams, write a

function showing the mass of the sample remaining after t years, where the annual

decay rate can be found from a constant in the function. Round all coefficients in the

function to four decimal places. Also, determine the percentage rate of decay per

year, to the nearest hundredth of a percent.

Question

Mathematics

Valerie

22 August, 21:01

Element X is a radioactive isotope such that every 38 years, its mass decreases by

half. Given that the initial mass of a sample of Element X is 890 grams, write a

function showing the mass of the sample remaining after t years, where the annual

decay rate can be found from a constant in the function. Round all coefficients in the

function to four decimal places. Also, determine the percentage rate of decay per

year, to the nearest hundredth of a percent.

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Answers (1)

Know the Answer?

Alyson Calhoun · Answer 1

f (x) = 890 (98.68) ^t-1

Step-by-step explanation:

the amount decays by 1.32% each year. So multiply by 98.68%, which is the remaining amount after 1 year.

f (x) = 890 (98.68) ^t-1

890 is your initial amount. Multiply that by 98.68 to get the remaining amount after 1 year. then multiply that to the power of t-1, t being the term number, or amount of years from the initial amount. You subtract by 1 because 890 (98.68) is already demonstrating the amount after the first term.