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The number of bacteria, b, in a refrigerated food is given by the function b(t) = 15t2 − 60t + 125, where t is the temperature of food in degrees Fahrenheit. The function t(h) = 3h + 4 gives the temperature, t, of the food h hours after being removed from the refrigerator. Find the number of bacteria in the food in h hours

Respuesta :

Edufirst
The number of bacteria, b:

        b(t) = 15t^2 − 60t + 125,

temperature, t:

        t(h) = 3h + 4

Find the number of bacteria in the food in h hours => you need to find b as a function of h, i.e. b(h) =  b[t(h)]

b [t (h)]= 15 [t(h) ]^2 - 60 [t(h)] + 125

     b(h) = 15 [ 3h + 4}^2 - 60 [3h + 4] + 125

     b(h) = 15[9h^2 + 24h + 16] - 180h - 240 + 125

     b(h) = 135h^2 + 360h + 240 - 180h + 125

b(h) = 135h^2 + 180h + 365 <---------- answer
W0lf93
b(t) = 15t2 - 60t + 125 
t(h) = 3h + 4
 So it follows that b(h) = b(t(h))
 Then 15(3h + 4)2 - 60 ( 3h + 4) + 125
 So b(h) = 15 (9h^2 + 24h + 16) - 60 ( 3h + 4) + 125
 b(h) = 135h^2 + 360h + 240 - 180h - 240 + 125
 b(h) = 135h^2 + 180h - 125

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