The number of bacteria, b, in a refrigerated food is given by the function b(t) = 15t2 − 60t + 125, where t is the temperature o f 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
2 answers:
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
<span>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 + 125b(h) = 135h^2 + 180h + 365 <---------- answer </span>
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