Question

I need help in an hour or less pls The number N of bacteria in a refrigerated food is given by N(T ) = 20T 2 – 80T + 500, 2 ≤ T ≤ 14 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) = 4t + 2, 0≤ t ≤ 3 where t is the time in hours. a. Find the composition (N ० T)(t) and interpret its meaning in context. To get the N number of T temperature, after is given in t in the time of hours. b. Find the time when the bacteria count reaches 2000.

Answer 1

The composition (N ∘ T)(t) represents the number of bacteria in the food at a certain time after it's removed from refrigeration modeled by N(t) = 20(4t + 2)^2 - 80(4t + 2) + 500. To find when the bacteria count reaches 2000, we solve the quadratic equation 2000 = 20(4t + 2)^2 - 80(4t + 2) + 500 for t.

Step-by-step explanation:

To solve for the composition (N ∘ T)(t), we must first substitute the equation for T(t) into N(T). The temperature of the food as a function of time is given by T(t) = 4t + 2. We can substitute this into N(T) to get N(4t+2), resulting in the following equation:

N(t) = 20(4t + 2)² - 80(4t + 2) + 500.

The composition function (N ∘ T)(t) models the number of bacteria N in the food at a certain time t after it has been removed from refrigeration. Now, to find when the bacteria count reaches 2000, we set N(t) to 2000 and solve for t:

2000 = 20(4t + 2)² - 80(4t + 2) + 500.

This is a quadratic equation in t, and by solving it, we will get the value of t when the bacteria count reaches 2000.