Applications of Exponential Equations Rumor Spreading: Given the function f(x) = 2 x to represent the number of people who have heard a rumor after x minutes. A)Find the number of people who have heard the rumor after 0, 1, 2, and 5 minutes. B)Graph f(x) on your calculator. Give the domain and range C)Give the amount of minutes it will take for the rumor to completely get around the high school.

Applications of Exponential Equations Viral Marketing Sound Familiar? – “Send this to 10 of your friends within an hour for good luck. If you you don’t a piano may fall from a building and land on top of your head!” A)Create an exponential function to express the chain viral marketing. Use x as the number of hours. B)Find the number of people who will receive the after 1,2,3, and 5 hours. C)About how many hours will it take for the entire USA to receive this ? D)Theoretically find the amount of time it will take for the entire population of Earth to receive the .

Applications of Exponential Equations The rapid development of the North Fork of Long Island has eliminated the natural predators of deer. Over the past 15 years, the deer population has exploded. The population increase, compounded with the removal of open space for housing, retail, etc has reduced the food supply for deer. Eventually the deer population will decline. The approximate deer population can be given as: D(x) = -.125x x , where x is the number of years since 1995.

Applications of Exponential Equations A college student quickly ingests 5 drinks at a party. The alcohol stays in the students bloodstream, even after he/she stops drinking. The function A(X) = -.015x x gives the approximate alcohol concentration (in tenths of a percent) in an average person’s bloodstream. In this function, x is the number of hours since the 5 drinks were ingested. This function is valid for the time frame from [0,8] hours.

Why do companies such as Budweiser, McDonald’s, and Coca-Cola advertise so much?

Applications of Exponential Equations Market research shows that under stable market conditions, sales will decrease at a rate unique to the product in the absence of advertising. Sales decline can be expressed by the function: » S F = S i (e) -at S F = Final Sales S i = Initial Sales A = rate of sales decline for that specific product t = years/months/etc

Applications of Exponential Equations Sales Decline – cont’d 1.Assume McDonald’s sales were $2 billion dollars last year. In the absence of advertising, sales would drop 8% per year. a.Find sales figures for the next 5 years. b.In what year would sales dip below $1 billion dollars?

Applications of Exponential Equations Sales Decline – cont’d The Lobster Roll has sales of $90,000 per weekend. Without advertising, the restaurant would lose 26% of sales each month. a.Find sales figures for the next 3 months. b.When would sales dip below $50,000 per weekend (What month)? c.Assume it costs the Lobster Roll $10,000 per weekend to run the restaurant, how many months until it goes out of business?