Question

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

$21,200. The anticipated profit for the end of the fourth year is $54,500. 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.
www.
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

Answer:P(x) = 129,200 + 2x

Step-by-step explanation:Here's the answer to your question:

Let's start by analyzing the information given:

1. Profit in the first year: $21,200

2. Anticipated profit in the fourth year: $54,500

3. Ratio of change in time to change in profit is constant.

From the given information, we can infer that the profit in the second year will be twice the profit in the first year, i.e., 2 x $21,200 = $42,400.

Similarly, the profit in the third year will be three times the profit in the first year, i.e., 3 x $21,200 = $63,600.

Now, let's write a linear function P(x) that expresses profit as a function of time x:

P(x) = 2x + 3(63,600 - 21,200)

= 2x + 3(42,400)

= 2x + 127,200

= 129,200 + 2x

Therefore, the linear function P(x) that expresses profit as a function of time x is:

P(x) = 129,200 + 2x

Note that the constant term is 129,200, which represents the profit in the first year. The coefficient of x is 2, which represents the ratio of change in time to change in profit.