Question

where is the mort t time t, Λ0 s the mDrt at bme t 0, and K s constant. ite o ' program that calculates the mort radioactive material. V hen executed the rogram12sks the userto onto he ha ife ofthe material in years the current amount o t e m en n b and the number of yc s from now or nch t e mort sh d be calcua ca cm th m rmation he prcgram in calcul toz the constan and then he amountこt years. For cu p the program c spla s ne messaoc he 교moum o he ma cr al af:er X years is X kg where X e he corresponding n marca va es Use the proram to determine how much plutonium 239 lh Flit 24.110 years》 wil be left from 5C lbafter 500 years.

Radioactive decay can be modeled by the equation
A=A0e−kt

where A is the amount at time t, A0 is the amount at time t = 0, and k is a constant. Write a MATLAB program that calculates the amount of a radioactive material. When executed, the program asks the user to enter the half-life of the material (in years), the current amount of the material (in lb), and the number of years t from now for which the amount should be calculated. From this information the program first calculates the constant k and then the amount at t years. For output the program displays the message: “The amount of the material after XX years is XX kg” where XX are the corresponding numerical values. Use the program to determine how much plutonium-239 (half-life 24,110 years) will be left from 50 lb after 500 years.

Answer 1

MATLAB CODE:

%Radioactive decay
t_half = input('Enter half life of the radioactive material(in years): ');
a_init = input('Enter current amount of the material (in lb): ');
t = input('Enter the number of years t from now for which the amount should be calculated: ');
a = a_init*exp(-(0.693/t_half)*t);
fprintf('The amount of the material after %.2f years is %.2f kg\n', t,a);

OUTPUT:

Enter half life of the radioactive material (in years) 50 Enter current amount of the material (in lb) 80 Enter the number of years t from now for which the amount should be calculated: 50 The amount of the material after 50.00 years is 40.01 kg