Answer: a) 389.915, b) 276.064.
Explanation:
Since we have given that
[tex]P'(t)=20(0.95)^t[/tex]
where t is the number of hours since the temperature changed.
(a) Write an integral that models the amount of bacteria at time t > 0.
[tex]\int\limits^\infty_0 {P'(t)} \, dt= \int\limits^\infty_0 {20(0.95)^t} \, dt=389.915[/tex]
(b) Find the amount after 24 hours.
It means 0<t < 24
[tex]\int\limits^{24}_0 {P'(t)} \, dt= \int\limits^{24}_0 {20(0.95)^t} \, dt=276.064[/tex]
Hence, a) 389.915, b) 276.064.
