Question

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 bacteria in the food in h hours. $b(t) = 15t^{2} - 60t + 125$

Answer 1

Answer: $b(t(h))=135h^2+180h+125$

Step-by-step explanation:

Given: The number of bacteria, B, in a refrigerated food is given by the function  $b(t)=15t^2-60t+125$ , 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.

Now, the number bacteria in the food in h hours is given by:-

$b(t(h))=15(3h+4)^2-60(3h+4)+125\\=15(9h^2+16+24h)-180h-240+125\\=135h^2+240+360h-180h-240+125\\=135h^2+180h+125$

So, The number bacteria in the food in h hours is given by:

$b(t(h))=135h^2+180h+125$