# Tutor profile: Amalia C.

## Questions

### Subject: Environmental Engineering

Describe the difference between the Environmental Protection Agency's National Primary Drinking Water Standards and the National Secondary Drinking Water Standards.

National Secondary Drinking Water Regulations (NSDWRs or secondary standards) are non-enforceable guidelines regulating contaminants that may cause cosmetic effects (such as skin or tooth discoloration) or aesthetic effects (such as taste, odor, or color) in drinking water. EPA recommends secondary standards to water systems but does not require systems to comply. However, states may choose to adopt them as enforceable standards. Please see for more information: https://www.epa.gov/ground-water-and-drinking-water/national-primary-drinking-water-regulations

### Subject: Calculus

The half-life of polonium-210 is 138 days. How long in days will it take for a sample of this substance to decay to 20% of its original amount? Use the exponential decay model, A(t) = (Initial Amount)e^(kt), to solve this exercise.

To use the exponential decay model, we first need the decay rate (k). Exponential decay is described by the first-order ordinary differential equation. Taking the natural log of both sides of this equation (remember it is an exponential decay) will yield: ln (Final Amount at time t / Initial Amount) = kt Solving for k, gives: k = [ ln (Af/Ai) ] / t Since we are given the half live (138 days) of polonium-210, we can use this value to find the element's rate of day ("k" in days) - Remember: If the problem is referring to the half-life, then the ratio of [Af/Ai] = 0.5 because half of the original sample has already undergone decay. k = [ ln 0.5 ] / 138 days = (-0.693)/138 = -0.00502 / day Armed with the exponential decay rate "k," let's look use the model to find how long it will take the element to decay to 20% of its original amount! Again use the equation: ln (Final Amount at time t / Initial Amount/) = kt and solve for time "t." t = [ ln (Af/Ai) ] / k Use k = -0.00502 / day (remember it is an exponential decay) & (Af/Ai) = 0.2 Therefore t (in days) = ln (0.2) / ( -0.00502 / day) = 320.6 days.

### Subject: Algebra

A certain beaker can hold 6 ounces of fluid without running over. If there is 2 4/5 ounces already in the beaker, how much can be added without overflowing the beaker?

This is a CBEST example word problem that boils down to subtracting fractions. In solving this problem, it will be useful to draw the solution to find how much volume is left in the beaker. Then you can visualize the solution and be able to subtract the fluid volume already in the beaker from the total volume the beaker can hold. First, use the rules for subtracting fractions after writing the fractions as improper fractions: 6 - 2 4/5 = 6/1 - 14/5 Then, using the bowtie method of adding and subtracting fractions, the answer will be: 3 1/5 ounces. Therefore, 3 and 1/5 ounces can be added to the beaker until it overflows.

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