Solve the problem.The monthly profit for a small company that makes long-sleeve T-shirts depends on the price per shirt. If the price is too high, sales will drop. If the price is too low, the revenue brought in may not cover the cost to produce the shirts. After months of data collection, the sales team determines that the monthly profit is approximated by f = -33p 2 + 1386p – 10,853, where p is the price per shirt and f is the monthly profit based on that price. Find the price that generates the maximum profit and find the maximum profit.

Use the change-of-base formula and a calculator to approximate the logarithm to 4 decimal places. 

Explain why a polynomial with real coefficients of degree 5 must have at least one real zero. 

Explain how the average rate of change of a function on the interval is related to slope. 

Solve the inequality.  Show work on your submission paper. 

Explain why the equation

Solve the problem on your submission paper.  f (x) =

Is the graph of

The half-life of carbon-14 is 5730 yr.  Find:  a) the decay rate of carbon-14.    b) if 20 g of carbon-14 is present now, how much will be left in 250 years? 

Use the graph of  to graph the function on your submission paper. Write the domain and range in interval notation.  Write the equation of any asymptote.