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It's a gross thought, but the number (N) of bacteria in refrigerated food is given by latex-  1≤T≤20 where T is the temperature of the food in degrees Celsius. When you take the food out of the refrigerator, the temperature of the food is given by T(t)=3t+2,   0≤t≤6 where t is the time in hours. Find the composition N(T(t)) and interpret what it means in this context.

Its a gross thought but the number N of bacteria in refrigerated food is given by latex 1T20 where T is the temperature of the food in degrees Celsius When you class=

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Given that the concentration of bacteria in the refrigerated food is

[tex]10T^2-20T-6----\mleft\lbrace1\mright\rbrace[/tex]

and the temperature of the food is given by

[tex]T(t)=3t+2-----\mleft\lbrace2\mright\rbrace[/tex]

Therefore, N(T(t) is given by

[tex]N\mleft(T(t)\mright)=10(3t+2)^2-20(3t+2)^{}-6[/tex]

Then,

[tex]\begin{gathered} N(T(t))=10(3t+2)^2-20(3t+2)^{}-6 \\ =10(9t^2+6t+6t+4)-60t-40-6 \\ =10(9t^2+12t+4)-60t-46 \\ =90t^2+120t+40-60t-46 \\ =90t^2+60t-6 \end{gathered}[/tex]

Answer: The composition is

[tex]N(T(t))=90t^2+60t-6[/tex]

It can be interpreted as the concentration of bacteria in the food when outside of the refrigerator with time.

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