Leading up to a big competition, a swim club plans a two-week decrease in their daily training, called “tapering,” so they will be rested and ready to swim their best. Each day, they will swim 5% less yards than the prior day.

1. How many yards will they swim the second day? The third?
2. If they swim 8,000 yards on the first day of taper, how many total yards will they swim over the two weeks?

Select all polynomials that have \((x+1)\) as a factor.

A car begins its drive in heavy traffic and then continues on the highway without traffic. The average cost (in dollars) of the gas this car uses per mile for driving \(x\) miles is \(c(x)=\frac{0.65+0.15x}{x}\). As \(x\) gets larger and larger, what does the end behavior of the function tell you about the situation?

Write a rational equation that cannot have a solution at \(x=2\).

For \(x\)-values of 0 and -1, \((x+1)^3 = x^3+1\). Does this mean the equation is an identity? Explain your reasoning.