According to the terms of Lavon’s insurance plan, he must...

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 muct the insurance company pays if $x$ represents Lavon's annual medical expenses.

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Key Concepts

Deductible

A deductible is the fixed amount that an insured individual must pay out-of-pocket before their insurance coverage begins to pay. In insurance problems, the deductible represents the initial cost burden on the policyholder before benefits apply.

Coinsurance

Coinsurance is the percentage of expenses that an insurance company pays after the deductible has been met. It is a cost-sharing mechanism between the insurer and the insured, meaning once the deductible is satisfied, the insurer pays a predetermined percentage of the remaining costs.

Piecewise Function

A piecewise function is a function defined by different expressions over various intervals of its domain. In insurance scenarios, such as when different conditions apply before and after the deductible threshold, a piecewise function is used to clearly outline the insurer's payment responsibility based on the total expenses.

Transcript

00:03 This question gives us a contextual situation revolving around levon and his medical expenses.

00:10 So we're told to let levon's expenses be represented by x.

00:16 So we're going to say however much his insurance expenses are, that's a total of x dollars.

00:21 And he has to pay, he pays the first $300 of his expenses.

00:29 So whatever his expenses are, he has to make it deductible basically.

00:32 He has to pay 300.

00:34 And then insurance, insurance will pay 80 % of what's left, of what's left of his expenses after that.

00:48 So we want to come up with a function that represents what the insurance pays.

00:53 So i'm going to call that function c of x that represents the insurance what they have to pay.

01:00 So it's a function that represents what they end up paying.

01:03 So let's think about this.

01:05 Levan's expenses are x dollars.

01:07 We don't know how much that is, but he's going to have to pay the first $300 of that.

01:13 So if we assume that levon has less than $300 in expenses, then the insurance doesn't pay anything, right? so the insurance is kind of on this.

01:27 If he has expenses that less than 300, we don't have to pay anything.

01:31 We only have to worry if he has expenses that are more than 300...

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