Question

Element X is a radioactive isotope such that every 30 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 4000 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. Function: f(t) = ( Submit Answer Growth % increase per year attempt 1 out of 2

Answer 1

dex = -loc dx = -ket Inx = kt + c x(t) = etc x(0)=C = 4000 x(t) = 4000e** x(30) = 2000 4000e-30k = 2000 2-30% - 2000 1 40002 -30k = 1 (1)

k=0.023104 k=0.0231 X(t) = 4000e-(0.0231 precentage of decay rate = axx100=-k x 100 = -2.31% growth=2.31%