Solve each problem. (Modeling) Lead IntakeAs directed by the 'Saf...

Question

Solve each problem. (Modeling) Lead IntakeAs directed by the 'Safe Drinking Water Act' of December 1974, the EPA proposed a maximum lead level in public drinking water of 0.05 mg per liter. This standard assumed an individual consumption of two liters of water per day.
(a)If EPA guidelines are followed, write an equation that models the maximum amount of lead A ingested in x years. Assume that there are 365.25 days in a year.

Accepted Answer

Hello, everyone. In this video, we're going to be looking at this parks problem where we want to write a linear equation where we represent the maximum amount of copper intake in X years and were given a couple of conversions Or units. The first is that the maximum copper level is a .5 mg per liter. And the average individual consumption is 2.5 L of water per day. And also there's 365 days in a year. So when we're looking at this question, the first thing I'm going to do is ask myself what it's looking for. So in this case, we want to represent the maximum amount of copper intake and the input that we're going to be putting into the equation is years. I'm not given the maximum copper level in years. I'm giving the maximum copper in leaders is the first Units here. It's 0.5 milligrams per leader. And from there, the second conversion I'm given is 2.5 L of water per day. I do 2.5 leaders per day. So now I have these two units and you can see that when I multiply them together. The leaders actually cancel out and I'm left with 1.25 because 0.5 times 2. is 1.25. And the units that I'm left with is milligrams per day. But in this case, you can see that I still don't have the years that I want to have because remember I want to have this number times X which is in units of years and I want to get back milligrams. So my output should be milligrams. In this case, I can't cancel out day and year because they're not the same unit. So I still need to do one more conversion. And that's where The assumption that there's days in one year comes into play. So I can say 1.25 mg per day, But there is 365 days in one year And notice how I wrote the 365 days in the numerator because I want to be able to cancel the unit of days. So once I do this multiplication, I have 1.2, 5 times 365. So this leaves me with 0.25. And now the units I have are milligrams per year. So now you can see that when I multiplied by the input variable X that they want, which is in years, the years unit cancels out and I'm left with milligrams, which is what we were looking for. So I can say that my equation see To represent the maximum amount of copper intake in next year's is equal to 456.25 x. And if we look at the answer choices, you can see that answer choice a also has 456.25 x. So hopefully this video helped and see you next time.

Key Concepts

Linear Modeling

Unit Conversion

Exponential Growth vs. Linear Growth

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