Question

Suppose a company's earnings are given by E(x)=P(x)+I(x), where x is the number of years since 2000, P(x) is the total profit from 2000 to year x, and I(x) is the intangible growth (the growth in value of the company's intangible assets such as its good name). If P(x)=1.8x+5 and I(x)=0.45x+3 for a certain company, determine the average earnings formula (earnings per year since 2000).

A(x)=____?_____

Answer 1

The average earnings formula, given the total profit and intangible growth functions, is A(x) = 2.25 + 8/x.

Step-by-step explanation:

To determine the average earnings formula for the company since the year 2000, we first need to add together the given formulas for total profit, P(x) = 1.8x + 5, and intangible growth, I(x) = 0.45x + 3. The sum of these two formulas gives us the overall earnings, E(x).

E(x) = P(x) + I(x)
= (1.8x + 5) + (0.45x + 3)
= 1.8x + 0.45x + 5 + 3
= 2.25x + 8

The average earnings per year, A(x), would be the overall earnings divided by the number of years, which is x. So:

A(x) = E(x) / x
= (2.25x + 8) / x.
When simplified, this expression gives an average earnings formula of:
A(x) = 2.25 + 8/x.