Write a clear and concise response to the following question (no more than 500 words). Should everyone exercise at least three times a week?

In the student's response I would look for a brief introduction to the topic of exercise, a thesis with 2-3 main points, a few sentences on each of the main points with supporting arguments, and a conclusion. A great response would include a brief section on potential counterarguments and rebuttals to those counterarguments.

In 2016 consumers in the United States bought 30 million television sets for $500 each. In 2017, consumers in the United States bought 35 million televisions at a price of $400 each. What is the price elasticity of demand for televisions in this market?

The price elasticity of demand measures how consumers respond to changes in the price of an item. Price elasticity of demand is calculated by dividing the % change in quantity demanded by the % change in price. Lets walk through the example. First we want to find the % change in quantity of televisions bought, which we do by subtracting the number of televisions sold in 2016 from the number of televisions sold in 2017 and dividing by the number of televisions sold in 2016. In numerical format this looks like: $$ \frac{35 million - 30million}{30million} = .167 $$. In this case we can leave the number in decimal format. Then we do the same for the % change in price: $$ \frac{$400 - $500}{$500} = -0.2 $$. Finally, to get the price elasticity of demand for televisions we divide the % change in quantity demanded by the % change in price and take the absolute value: $$ |\frac{.167}{-0.2}| = 0.835 $$

Please find the inverse of the given function: $$ f(x) = 10x - 5 $$

To find the inverse of a function start by replacing $$ f(x) $$ with $$ y $$ and then switch the x and the y so that the equation looks like $$ x = 10y - 5 $$. Now solve for $$ y $$. To do this, add $$ 5 $$ to both sides of the equation to get $$ x + 5 = 10y $$ then divide both sides by $$ 10 $$ to get $$ \frac{x + 5}{10} = y $$. Now that we have our final inverse function, we have to put it in proper format with the inverse notation: $$ f^{-1}(x) = \frac{x+5}{10} $$