Just Peachy Orchard produced 1100 bushels of peaches last year. This year the owner earned $8800 from sales. He's thinking that the number of bushels produced will increase by a growth factor of 1.1 each year and his sales will increase by a factor of 1.111 each year. If B(t)= 1100(1.1)t represents the number of bushels produced t years from now and S(t) = 8800(1.111)t represents the owner's income t years from now, which function, as defined by P(t), represents the price for one bushel of peaches t years from now?

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pedrocarratore pedrocarratore · Answer 1 · 2019-12-13T04:34:31+01:00

Answer:

[tex]P(t) ={8*(1.01)^t}[/tex]

Step-by-step explanation:

The number of bushels produced is given by:

[tex]B(t)= 1100(1.1)^t[/tex]

The owner's income is given by:

[tex]S(t) = 8800(1.111)^t[/tex]

Income is given by the price per unit multiplied by the number of units sold. Therefore, the price function can be represented as:

[tex]P(t) =\frac{S(t)}{B(t)} \\P(t) =\frac{8800(1.111)^t}{1100(1.1)^t} \\P(t) =\frac{8*1100(1.1)^t*(1.01)^t}{1100(1.1)^t}\\P(t) ={8*(1.01)^t}[/tex]