Respuesta :
Answer:
[tex]N(T(t))=432t^2-374.4t-118.88[/tex]
The number of Bactria after 5.8 hours is 12242.
Step-by-step explanation:
The number of bacteria in a refrigerated food product is given by
[tex]N(T)=27T^2-180T+100[/tex]
where, T is the temperature of the food.
When the food is removed from the refrigerator, then the temperature is given by
[tex]T(t)=4t+1.6[/tex]
We need to find the composite function N(T(t)).
[tex]N(T(t))=N(4t+1.6)[/tex]
[tex]N(T(t))=27(4t+1.6)^2-180(4t+1.6)+100[/tex]
[tex]N(T(t))=432t^2+345.6t+69.12-720t-288+100[/tex]
[tex]N(T(t))=432t^2-374.4t-118.88[/tex]
where N(T(t)) is the number of bacteria after t hours.
Substitute t=5.8 in the above function.
[tex]N(T(5.8))=432(5.8)^2-374.4(5.8)-118.88[/tex]
[tex]N(T(5.8))=14532.48-2290.4[/tex]
[tex]N(T(5.8))=12242.08[/tex]
[tex]N(T(5.8))\approx 12242[/tex]
Therefore, the number of Bactria after 5.8 hours is 12242.
