Question

❗️❗️❗️OFFERING LOTS OF POINTS❗️❗️❗️❗️A fruit company recently released a new applesauce. By the end of its first year, profits on this product amounted to

$39,800. The anticipated profit for the end of the fourth year is $83,900. After the first year, the ratio of change in time
to change in profit is constant. Let x be years and P be profit in dollars.
a. Write a linear function P(x) that expresses profit as a function of time.
P(x)=
(Use integers or fractions for any numbers in the equation. Do not include the $ symbol in your answer.)

Answer 1

To find a linear function P(x) that expresses profit as a function of time, we need to find the slope of the line that represents the relationship between profit and time. The slope is defined as the change in y (profit) over the change in x (time).

In this case, the change in time is 4 years and the change in profit is $83,900 - $39,800 = $44,100. Therefore, the slope of the line is $44,100 / 4 years = $11,025/year.

Now that we have the slope, we can use the point-slope formula to find the linear function P(x):

P(x) = $11,025/year * x + b

We need to find the value of b that makes this equation correct for the given starting point (x = 1 year, P = $39,800). Plugging these values into the equation, we get:

$39,800 = $11,025/year * 1 year + b

Solving for b, we get:

b = $39,800 - $11,025/year * 1 year = $28,775

So the linear function that expresses profit as a function of time is:

P(x) = $11,025/year * x + $28,775