SOLUTION: Element X is a radioactive isotope such that it’s mass decreases by 11% every year. If an experiment starts out with 530 grams of Element X, write a function to represent the mas

Question 1172664: Element X is a radioactive isotope such that it’s mass decreases by 11% every year. If an experiment starts out with 530 grams of Element X, write a function to represent the mass of the sample after t years, where the quarterly rate of change can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percent rate of change per quarter, to the nearest hundredth of a percent.
Function: f(t)= ____ (___) ^ __
____ <- growth or decay?
____ % <- increase per quarter
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

11% is lost each year, so each year the amount remaining is 100-11 = 89% of the amount at the beginning of the year. So the amount remaining gets multiplied by 89% = 0.89 each year.

So starting with 530 grams, after t years the amount remaining is

The portion remaining after a quarter of a year is, to a few decimal places,

So the decrease per quarter is

or 2.87%.

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