function composition application\nthe number of bacteria in a refrigerated food product is given…

function composition application\nthe number of bacteria in a refrigerated food product is given by\nn(t)=21t² - 125t + 37, 6 < t < 36\nwhere t is the temperature of the food in degrees fahrenheit and n(t) is the number of bacteria.\nthe food product is removed from the refrigerator and its temperature can be modeled by the function t(t)=5t + 2, where t is the time in hours and t(t) is the temperature in degrees fahrenheit.\nusing these two functions, determine the composite function that gives the number of bacteria in a food product as a function of its temperature.\ngiven n(t)=21t² - 125t + 37 and t(t)=5t + 2, find the composite function n(t(t)).\nnote: you do not need to simplify your answer\nn(t(t))=\nusing the composite function n(t(t)), determine the number of bacteria in a food product 1 hours after the food is removed from the refrigerator. write your answer as an ordered pair and interpret your answer in a complete sentence.\nnote: you must use units in both parts of your sentence.\nordered pair:\nafter the food product is removed from the refrigerator, it will contain approximately (do not put commas in your answer)

function composition application\nthe number of bacteria in a refrigerated food product is given by\nn(t)=21t² - 125t + 37, 6 < t < 36\nwhere t is the temperature of the food in degrees fahrenheit and n(t) is the number of bacteria.\nthe food product is removed from the refrigerator and its temperature can be modeled by the function t(t)=5t + 2, where t is the time in hours and t(t) is the temperature in degrees fahrenheit.\nusing these two functions, determine the composite function that gives the number of bacteria in a food product as a function of its temperature.\ngiven n(t)=21t² - 125t + 37 and t(t)=5t + 2, find the composite function n(t(t)).\nnote: you do not need to simplify your answer\nn(t(t))=\nusing the composite function n(t(t)), determine the number of bacteria in a food product 1 hours after the food is removed from the refrigerator. write your answer as an ordered pair and interpret your answer in a complete sentence.\nnote: you must use units in both parts of your sentence.\nordered pair:\nafter the food product is removed from the refrigerator, it will contain approximately (do not put commas in your answer)

Answer

Explanation:

Step1: Substitute $T(t)$ into $N(T)$

$N(T(t))=21(5t + 2)^2-125(5t + 2)+37$

Step2: Find temperature at $t = 1$

First, find $T(1)$: $T(1)=5\times1 + 2=7$ (degrees Fahrenheit)

Step3: Find number of bacteria at $t = 1$

Substitute $t = 1$ into $N(T(t))$: $N(T(1))=21(5\times1 + 2)^2-125(5\times1 + 2)+37=21\times7^2-125\times7 + 37=21\times49-875+37=1029-875+37 = 191$

Answer:

$N(T(t))=21(5t + 2)^2-125(5t + 2)+37$ Ordered Pair: $(1,191)$ After the food product is removed from the refrigerator for 1 hour, it will contain approximately 191 bacteria.