Question

The rate at which radioactive waste is entering the atmosphere at time t is decreasing and is given by Pe^-kt, where P is the initial rate. Use the improper integral

∫^[infinity]_0 Pe^-kt dt
with P = 50 to find the total amount of the waste that will enter the atmosphere for each value of k.
k=0.06

Answer 1

8333.33

Explanation:

Given that the rate at which radioactive waste is entering the atmosphere at time t is decreasing and is given by Pe^-kt, where P is the initial rate. Use the improper integral

∫^[infinity]_0 Pe^-kt dt

with P = 50 to find the total amount of the waste that will enter the atmosphere for each value of k.

k=0.06

Hence the total amount of waste that can enter the atmosphere when k =0.06 is given by

`\int\limits^(\infty) _0 {50e^(-0.06t) } \, dt\\=-(50)/(0.006) e^(-0.06t)`

Substitute limits

=8333.33