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

Answer:

8333.33

Step-by-step 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

$\int\limits^{\infty} _0 {50e^{-0.06t} } \, dt\\=-\frac{50}{0.006} e^{-0.06t}$

Substitute limits

=8333.33