Question

The fruit company recently released a new apple sauce. by the end of its first year, profits on this product amounted to $24,400. The anticipated profit for the end of the fourth year is $39,700. after the first year, the ratio change in time to change in profit is constant. Let x be years and P be profit in dollars. Write a linear function P(x) that expresses profit as a function of time. P(x)= ___

Answer 1

To write the linear function P(x) that expresses profit as a function of time, we use the slope formula and point-slope form of a linear equation. Therefore P(X)= 5100x + 19300

Step-by-step explanation:

To write a linear function expressing profit as a function of time, we need to find the equation of a straight line that passes through two points. Using the given information, we can form two points with the coordinates (1, 24400) and (4, 39700), where x represents the years and P represents the profit in dollars.

Using the slope formula, we find the slope of the line to be:

m = (39700 - 24400) / (4 - 1) = 15300 / 3 = 5100

Now, we can use the point-slope form of a linear equation to find the equation of the line:

P - 24400 = 5100(x - 1)

Simplifying the equation, we get:

P = 5100x + 19300