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`

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`