1. The annual revenue of the fitness cycling company Peloton in millions of dollars can be modeled by the equation P(t)=170(2.35)' where t represents the years since 2016. What is the growth factor? а. What is the annual growth/decay rate in percent? b. Algebraically determine in which year the annual revenue of Peloton will reach 900 million dollars. с. ()) *100- An advertising agency conducted a survey and found that the number of units sold, N , depends on the amount a, spent on advertising (in dollars). The following table gives the amount spent on advertising and the number of units sold accordingly. Source: The Nature of Mathematics, 10e, Smith, K.J. 3. Amount Spent (S) Number of Units Sold 3,572 3,902 4,055 1000 2 3000 5000 4,156 7000 Using a calculator, make a scatter plot of the data, where x represents the amount of money spent. Using your calculator, find the logarithmic regression (LnReg) that models this situation. Call this equation N(a), and round values to the nearest whole number. а. M0 According to the model N(a), how many units are sold if $8,000 is spent on advertising? b. Using the model N(a), algebraically determine how much money needs to be spent on advertising in order to sell 5,000 units. You may check your answer graphically. с. Fall 2019 350

The demand for ceiling fans can be modeled below as D(p) = 25.62(0.996P) thousand ceiling fans where p is the price (in dollars) of a ceiling fan. (a) According to the model, is there a price above which consumers will no longer purchase fans? Explain why or why not. The model is exponential and ---Select--- ✓the horizontal axis. Therefore there ---Select--- above which consumers will not purchase a ceiling fan. (b) Calculate the amount that consumers are willing and able to spend to purchase 17 thousand ceiling fans. (Round your answer to three decimal places.) thousand (c) How many fans will consumers purchase when the market price is $100? (Round your answer to three decimal places.) thousand fans (d) Find the consumers' surplus when the market price is $100. (Round your answer to three decimal places.) thousand

According to the U.S. Census Bureau, the population of the United States in 2008 was 304 million people. In addition, the population of the United States was growing at a rate of 1.1% per year. Assuming this growth rate continues, the model P(t) = 304 · (1.011)* - represents the population P (in millions of people) in year t. According to the model, when will the population be 407 million people? Be sure to round your answer to the nearest whole year. Year

_17. Write an exponential function to model the situation. Tell what each variable represents. A price of Php 125.00 increases 4% each year. A. P = 125(1.04 )* where P-price and x-years В. P = 125(1.04)* where P=years and x-price С. P = 1.04(125 )* where P=price and x=years P = 125(1.04) where P=price D.