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Question 479968: The number of bacteria in a quarter teaspoon of potato salad left in the sun on the picnic table is given by N(T)= 35T^2 - 10T +10000, 1 less than (<) or equal to T less than (<) or equal to 20 where T is the ambient air temperature. When the food is placed on the table at noon, the increase in air temperature as a function of time can be modeled by the equation T (t) = 3t +10, 0 less than (<) or equal to t less than or equal to3, where t is the time in hours.
1.
Find the composite function N(T(t))
2.In a well structured sentecnce(s), interpret the composition
3.
How many bacteria are in the quater teaspoon of potato salad after it has set in the sun for two hours?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The number of bacteria in a quarter teaspoon of potato salad left in the sun on the picnic table is given by N(T)= 35T^2 - 10T +10000, 1 <= T <= 20 where T is the ambient air temperature.
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When the food is placed on the table at noon, the increase in air temperature as a function of time can be modeled by the equation T(t) = 3t +10, 0 <= t <=3, where t is the time in hours.
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1. Find the composite function N(T(t)) =
N(t) = 35(3t+10)^2-10(3t+10) + 10000
N(t) = 35[9t^2+60t+100] - 30t - 100 + 10000
N(t) = 315t^2 + 2100t + 3500 - 30t -100 + 10000
N(t) = 315t^2 + 2070t +13400
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2.In a well structured sentence(s), interpret the composition
N(T(t)) gives you the bacteria count as a function of elapsed time.
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3.How many bacteria are in the quarter teaspoon of potato salad after it has set in the sun for two hours?
N(2) = 18800
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Cheers,
Stan H.
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