Respuesta :
Answer:
The expression is given as:
[tex]H(t)=C(t)\times F(t)=240\times 3^t[/tex].
Step-by-step explanation:
Sophia expects the number of cows, C, on her farm t years from now to be modeled by the function:
[tex]C( t ) = 30\times (2)^t[/tex]
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
[tex]F( t ) =8\times (1.5)^t[/tex]
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)
[tex]H(t)=30\times 8\times (2)^t\times (1.5)^t[/tex]
and we know that [tex]a^x\times b^x=(a\times b)^x=(ab)^x[/tex]
Hence,[tex]H(t)=240\times (2\times 1.5)^t\\\\H(t)=240\times 3^t[/tex].
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:
[tex]H(t)=C(t)\times F(t)=240\times 3^t[/tex].
