Question

The revenue each season from tickets at the theme part is represented by t(x) = 5x. The cost to pay the employees each season is represented by r(x) = (1. 5)x. Examine the graph of the combined function for total profit and estimate the profit after four seasons.

Answer 1

The total profit after four seasons is 35.0

Function

The functions are given as:

• Revenue function: $t(x) = 5x$.
• Cost function: $r(x) = 1.5x$.

Profit function

The profit function p(x) is calculated using:

$p(x) = t(x) -r(x)$

So, we have:

$p(x) = 5x -1.5x$

Evaluate the differences

$p(x) = 3.5x$

Total Profit

Evaluate the values of the function from x =1 to 4

• $p(1) = 3.5$.
• $p(2) = 7.0$.
• $p(3) = 10.5$.
• $p(4) = 14.0$

So, the total profit is:

$Total =p(1) + .....+p(4)$

This gives

$Total =3.5 + 7.0 + 10.5 +14.0$

$Total =35.0$

Hence, the total profit after four seasons is 35.0

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