Question

A fruit company recently released a new applesauce. By the end of its first year, profits on this product amounted to $39,200. The anticipated profit for the end of the fourth year is $76,400. The ratio of change in time to

change in profit is constant. Let x be years and y be profit.
a. Write a linear equation y that expresses profit in terms of x.
b. Use this equation to predict the company's profit at the end of the seventh year.
c. Predict when the profit should reach $88,800.

Answer 1

a. y = 12400x + 26800

b. $113600

c. end of the 5th year

Explanation:

a.

We are given 2 points, (1, 39200) and (4, 76400).

We are looking for the equation of the line that passes through those two points.

slope = (76400 - 39200)/(4 - 1) = 12400

y = mx + b

y = 12400x + b

We have when x = 1 y = 39200.

39200 = 12400(1) + b

b = 26800

The equation is

y = 12400x + 26800

b.

y = 12400x + 26800

x = 7

y = 12400(7) + 26800

y = 113600

c.

y = 12400x + 26800

88800 = 12400x + 26800

62000 = 12400x

x = 5