Avery predicts that the number of horses, HHH, on her farm ttt years from now will be modeled by the function H(t)=25(2)^tH(t)=25(2) t H, left parenthesis, t, right parenthesis, equals, 25, left parenthesis, 2, right parenthesis, start superscript, t, end superscript, and that the amount of hay, AAA, in tons, that she produces on her farm ttt years from now will be modeled by the function A(t)=150(1.5)^tA(t)=150(1.5) t A, left parenthesis, t, right parenthesis, equals, 150, left parenthesis, 1, point, 5, right parenthesis, start superscript, t, end superscript. Let FFF be the predicted yearly supply of hay, in tons, available to each horse in Avery's farm ttt years from now. Note that the hay produced on Avery's farm is used exclusively to feed her horses. Write a formula for F(t)F(t)F, left parenthesis, t, right parenthesis in terms of H(t)H(t)H, left parenthesis, t, right parenthesis and A(t)A(t)A, left parenthesis, t, right parenthesis.

Question

11-10-2018
Mathematics

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Avery predicts that the number of horses, HHH, on her farm ttt years from now will be modeled by the function H(t)=25(2)^tH(t)=25(2) t H, left parenthesis, t, right parenthesis, equals, 25, left parenthesis, 2, right parenthesis, start superscript, t, end superscript, and that the amount of hay, AAA, in tons, that she produces on her farm ttt years from now will be modeled by the function A(t)=150(1.5)^tA(t)=150(1.5) t A, left parenthesis, t, right parenthesis, equals, 150, left parenthesis, 1, point, 5, right parenthesis, start superscript, t, end superscript. Let FFF be the predicted yearly supply of hay, in tons, available to each horse in Avery's farm ttt years from now. Note that the hay produced on Avery's farm is used exclusively to feed her horses. Write a formula for F(t)F(t)F, left parenthesis, t, right parenthesis in terms of H(t)H(t)H, left parenthesis, t, right parenthesis and A(t)A(t)A, left parenthesis, t, right parenthesis.

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erato erato · Answer 1 · 2018-10-20T14:05:12+02:00

Number of Horses in Avery's farm, after t years from now is given by function H(t); where [tex]H(t) = 25(2)^{t}[/tex]

The amount of hay, in tons, that is produced on her farm t years from now is given by function A(t); where [tex]A(t) = 150(1.5)^{t}[/tex]

The predicted yearly supply of hay, in tons, available to each horse in Avery's farm t years from now is given by function F(t); where F(t) = A(t)/H(t)

So, F(t) = [tex]\frac{150(1.5)^{t}}{25(2)^{t}}[/tex] = [tex]6 (\frac{1.5}{2}) ^{t}[/tex] = [tex]6 (0.75)^{t}[/tex] tons/horse