Answer:
11,713 bacteria
Step-by-step explanation:
Integrating the growth rate function gives us the population of bacteria at any given moment 't', in hours:
[tex]r(t) = (450.263)e^{1.12567t} \\\int\ {r(t)} \, dt =P(t) = \frac{450.263}{1.12567}*e^{1.12567t} +C[/tex]
Since at t=0, P(t) = 400, the value of C is:
[tex]P(0) = \frac{450.263}{1.12567}*e^{1.12567*0} +C\\400 = 400*1+C\\C=0[/tex]
The number of bacteria after 3 hours is:
[tex]P(3) = 400*e^{1.12567*3}\\P(3) =11,713[/tex]
