Sophia expects the number of cows, c c, on her farm t t years from now to be modeled by the function c ( t ) = 3 0 ( 2 ) c(t)=30(2) t . additionally, she expects the supply of hay, f f, in tons, that her crops can provide for each cow t t years from now to be modeled by the function f ( t ) = 8 ( 1 . 5 ) f(t)=8(1.5) t . let h h be the total yearly amount of hay produced in sophia's farm (in tons) t t years from now. note that the hay produced on sophia's farm is used exclusively to feed her cows. write the formula of h ( t ) h(t) in terms of c ( t ) c(t) and f ( t ) f(t).

The expression is given as:

.

Step-by-step explanation:

Sophia expects the number of cows, C, on her farm t years from now to be modeled by the function:

Additionally, she expects the supply of hay, F, in tons, that her crops can provide for each cow t years from now to be modeled by the function

Let H be the total yearly amount of hay produced in Sophia's farm (in tons) t years from now.

Total amount of Hay produced in sophia's farm= Number of cows in farm×Amount of hay required for each cow.

i.e. H(t)=C(t)×F(t)

and we know that

Hence,.

Hence, the hay produced on Sophia's farm is used exclusively to feed her cows i.e. we need to write the formula of H ( t ) in terms of C(t) and F (t) is:

.

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