Question

a local fruit company recently released a new flavor of applesauce by the end of the first year profits on this product amounted to 28,000.00 the anticipated profits for the end of the third year is 56,000.00 assume that the rate of profit will remain constant over time with p representing the profit and x representing the number of years.A) write a linear function p(x) that expresses profit as a function of time. P(x)=_______B) use the function in (a) to predict the companys profit at the end of the seventh $ ________C) use the function in (a) to predict when companys profit should reach 266,000.00_____years

Answer 1

Given data:

The given profit earned at the end of first year is p=28,000.

The profit earned at the end of third year is p'=56,000.

The expression for the profict function is,

p(x)-p=(p'-p)(x-t)/(t'-t)

Substitute 3 fot t', 1 for t, and other given values in the above expression.

p(x)-28000=(56,000-28,000)(x-1)/(3-1)

p(x)-28000=28,000(x-1)/2

p(x)-28000=14,000(x-1)

p(x)=14,000x+28,000-14,000

p(x)=14,000x+14,000

=14,000(x+1)

Thus, the expression for the profit function is p(x)=14,000(x+1).