Q48. - Algebra 2

Question

According to the terms of Lavon’s insurance plan, he must pay the first $300 of his annual medical expenses. The insurance company pays 80% of the rest of his medical expenses. Write a function for how much the insurance company pays if x represents Lavon’s annual medical expenses.

Step-by-Step Solution

Answer

The required function is: $y=\{\begin{array}{l}0if0\le x\le 300\\ 0.8(x-300)ifx>300\end{array}$

Step-1 – Absolute value of the function.

Absolute value - The absolute value of a number is its distance of number from zero on the number line and distance is always non-negative  

Step-2 – Determine the given value

Let the annual medical expenses is x

Let the payment made by insurance company is y

Now, if medical expenses x is less than or equal to $300 then the insurance company y will not pay anything. i.e. $y=0,x\le 300$

Now, if medical expenses x is more than or equal to $300 then the insurance company y will pay 80% of remaining.

$\begin{array}{l}y=\frac{80}{100}(x-300)\\ y=0.8(x-300)\end{array}$

Step-3 – Determine the Function for given value.

The required function is: $y=\{\begin{array}{l}0if0\le x\le 300\\ 0.8(x-300)ifx>300\end{array}$