You have just opened a new night club, Russ' Techno pit stop, but are unsure how high to set cover charge. One week, per guest and average 300 guest per night. The next week you charged $15 per guest and average 250 guest per night. Find a linear demand equation showing the number of guest q per night as a function of the cover charge P. Find the nightly revenue R as a function of the cover charge p Club $3 C per head. In addition, alcoholic drinks for each guest, costing, the $3000 addition the nightly overhead (rent, salaries. DJ, etc.) amount to find the cost C as a function of the cover charge p. Now, find the profit in terms of the cover charge p, and hence determine the cover charge you should charge for a maximum profit. Assume that you invest $7,000 at an annual interest rate 4.5%. How long must you wait before your investment be worth 524,000 if the interest is compounded continuously? A bacteria culture starts with 2000 bacteria and triples in size every 2 hours. Find an exponential model for the size of the culture as a function of time t in hours Use this model to predict how many bacteria there will be after 18 hours How many hours will it take for the culture size to become 100,000 bacteria