Cost of employee parking provided by a large firm has been increasing over the years. A business analyst approximates the yearly parking cost by an exponential function. Using P as the yearly parking cost in thousands of dollars and t as the number of years since 2015 (when the firm moved into the current location), the business analyst determines the parking cost function to be P(t) = 65(1.3)' . Find P'(t), the rate at which the parking cost is increasing according to the business analyst's model. Rate of change P'(t) =| thousands of dollars/yr

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

If the population of a Nigeria doubles in 9 years, find the growth rate k. Assume that the population increases exponentially.

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