Chapter 2: Q48. (page 94)

According to the terms of Lavon鈥檚 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 ifx represents Lavon鈥檚 annual medical expenses.

Expert verified

The required function is: $y = {\begin{cases} 0 鈥夆赌夆赌� i f 鈥夆赌夆赌� 0 鈮� x 鈮� 300 \\ 0.8 (x 鈭� 300) 鈥夆赌� i f 鈥夆赌� x > 300 \end{cases}$

Step by step solution

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

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. $y = 0, x 鈮� 300$

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

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

The required function is: $y = {\begin{cases} 0 鈥夆赌夆赌� i f 鈥夆赌夆赌� 0 鈮� x 鈮� 300 \\ 0.8 (x 鈭� 300) 鈥夆赌� i f 鈥夆赌� x > 300 \end{cases}$

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