Question

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?

Answer 1

`P(t) ={8*(1.01)^t}`

Explanation:

The number of bushels produced is given by:

`B(t)= 1100(1.1)^t`

The owner's income is given by:

`S(t) = 8800(1.111)^t`

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

`P(t) =(S(t))/(B(t)) \\P(t) =(8800(1.111)^t)/(1100(1.1)^t) \\P(t) =(8*1100(1.1)^t*(1.01)^t)/(1100(1.1)^t)\\P(t) ={8*(1.01)^t}`