Respuesta :
Answer:
11,513
Explanation:
Data provided in the question:
Initial bacteria = 200
Growth rate r(t) = [tex](450.268)e^{1.12567t}[/tex]
Now,
Total growth after 3 hours = [tex]\int\limits^3_0 {(450.268)e^{1.12567t}} \, dt[/tex]
or
Total growth after 3 hours = [tex]450.268\int\limits^3_0 {e^{1.12567t}} \, dt[/tex]
or
Total growth after 3 hours =[tex]450.268[\frac{e^{1.12567t}}{1.12567}]^3_0[/tex]
[ ∵ [tex]\int{d(e^x)}{dt}=\frac{e^x}{\frac{dx}{dt}}[/tex]]
Thus,
Total growth after 3 hours = 400 × [tex][{e^{1.12567t}]^3_0[/tex]
or
Total growth after 3 hours = 400 × [tex][{e^{1.12567(3)}-e^{1.12567(0)}][/tex]
or
Total growth after 3 hours ≈ 11313
Hence,
Total bacteria after 3 hours = Initial bacteria + Total growth after 3 hours
= 200 + 11313
= 11,513
