Question

85. Biology The number of bacteria in a refrigerated food product is given by N(T) = 1072-20T + 600, 1 T 20 where T is the temperature of the food in degrees Celsius. When the food is removed from the refrigerator, the temperature of the food is given by Tt) 2t + 1 where t is the time in hours. (a) Find the composite function N(T(d) or (N-T)(t) and interpret its meaning in the context of the situation. (b) Find (N。T)(12) and interpret its meaning. (c) Find the time when the bacteria count reaches 1200.

Need an assist on this problem. Show work.

Answer 1

a)

We have to find the composite function :

where ,

N(T) = 107-2-20T+ 600
,           
<T <20

T(t) = 2t+ 1

Now,

(Mo T)(t) = 10(2t + 1)2-20(2t + 1) + 600

10(4t2 + 4t + 1) _ 40t-20 + 600

40t2 + 40t 10-40t-20 + 600

                  ...1)

(Mo T)(t) 40t2 +590

this shows the number of bacteria at time t

b)

Now we have to find

(Νο Τ)(12)

for that we will plug t=12 in equation 1

(No T)(12) = 40(12)2+590

this shows that number of bacteria at time t=12 hour

c)

Now we have to find the time when bacteria count N(t) =1200

we will plug N(t) =1200 in equation 1 , we get:

1200 40 + 590

shifting 590 to left side

1200-590 = 40

$40t^2=610$

dividing both sides by 40

$t^2=rac{610}{40}$

$t^2=15.25$

we will ignore negative value as time cannot be negative so when t=3.9051 hr, number of bacteria is 1200