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 <= 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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