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.

Verified step by step guidance

1. Start by identifying the daily lead intake based on the EPA's maximum lead level: 0.05 mg per liter and 2 liters per day.
2. Calculate the daily lead intake: $0.05\text{ mg/L}\times 2\text{ L/day}=0.1\text{ mg/day}$.
3. Determine the annual lead intake by multiplying the daily intake by the number of days in a year: $0.1\text{ mg/day}\times 365.25\text{ days/year}$.
4. Express the total lead intake over $x$ years by multiplying the annual intake by $x$: $A=(0.1\times 365.25)\times x$.
5. Write the final equation for the maximum amount of lead $A$ ingested in $x$ years: $A=36.525x$.

Key Concepts

Linear Modeling

Linear modeling involves creating a mathematical equation that represents a real-world situation. In this case, the equation will relate the amount of lead ingested over time to the maximum allowable concentration in drinking water. Understanding how to set up a linear equation based on given parameters is crucial for solving the problem.

Unit Conversion

Unit conversion is the process of changing one set of units to another, which is essential in this problem to ensure consistency. Here, we need to convert the lead concentration from mg per liter to total lead ingested over a specified time frame, taking into account daily water consumption and the number of days in a year.

Exponential Growth vs. Linear Growth

Understanding the difference between exponential and linear growth is important in modeling scenarios like lead intake. In this case, the lead intake is modeled linearly over time, as it accumulates at a constant rate based on daily consumption. Recognizing this distinction helps in accurately interpreting the results of the model.