The number N of bacteria in a refrigerated food is given by $N ( T ) = 10 T ^ { 2 } - 20 T + 600,1 \leq T \leq 20$ where T is the temperature of the food in degrees Celsius.When the food is removed from refrigeration, the temperature of the food is given by $T ( t ) = 3 t + 2,0 \leq t \leq 6$ where t is the time in hours. Find the bacteria count after 0.5 hour.

A)About 565 bacteria
B)About 793 bacteria
C)About 653 bacteria
D)About 390 bacteria
E)About 705 bacteria

Question

The number N of bacteria in a refrigerated food is given by $N ( T ) = 10 T ^ { 2 } - 20 T + 600,1 \leq T \leq 20$ where T is the temperature of the food in degrees Celsius.When the food is removed from refrigeration, the temperature of the food is given by $T ( t ) = 3 t + 2,0 \leq t \leq 6$ where t is the time in hours. Find the bacteria count after 0.5 hour.
 
A)About 565 bacteria
B)About 793 bacteria
C)About 653 bacteria
D)About 390 bacteria
E)About 705 bacteria

Quizplus · Accepted Answer

First, find the temperature of the food after 0.5 hour using $T(t) = 3t + 2$. Substituting $t = 0.5$ gives $T(0.5) = 3(0.5) + 2 = 3.5$. Then, use this temperature to find the number of bacteria using $N(T) = 10T^2 - 20T + 600$. Substituting $T = 3.5$ gives $N(3.5) = 10(3.5)^2 - 20(3.5) + 600 = 122.5 - 70 + 600 = 652.5$, which rounds to about 653 bacteria.

The Number N of Bacteria in a Refrigerated Food Is N(T)=10T2−20T+600,1≤T≤20N ( T ) = 10 T ^ { 2 } - 20 T + 600,1 \leq T \leq 20N(T)=10T2−20T+600,1≤T≤20

The Number N of Bacteria in a Refrigerated Food Is $N ( T ) = 10 T ^ { 2 } - 20 T + 600,1 \leq T \leq 20$