Consider the following table of values of the functions f and g and their derivatives at various points. a. Find D,(fig(x)]) at x = 4. b. Find D, (off(x)]) at x =3 D, (fig(x)]) at x = 4 is (Type an integer or a simplified fraction.) f(x) 2 P (xx) 4 3 2 4 g(x) 3 4 - 7 - 8 g'(x) 5 /8 7/8 1/8 2 3/8 Suppose the demand for a certain brand of a product is given by D(P) = 10+450, where p is the price in dollars. If the price, in terms of the cost c, is expressed as p(c) = 3c-9, find the demand function in terms of the cost D(c) = 2. 3 The growth in the number (in millions) of Internet users in a certain country between 1990 and 2015 can be approximated by a logistic function with k = 0.0014, where t is the number of years since 1990. In 1990 (when t = 0), the number of users was about 3 million, and the number is expected to level out around 230 million. (a) Find the growth function G(t) for the number of Internet users in the country. (b) 1995 Estimate the number of Internet users in the country and the rate of growth for the following years. (c) 2000 (d) 2011 (e) What happens to the rate of growth over time? (a) G(1) = (Type an exact answer in terms of e.) (b) The number of Internet users in the country in 1995 is million. (Type an integer or decimal rounded to one decimal place as needed.) Find G'(1). Round any coefficients that are not part of exponents to the nearest integer. G'(1) = (Type an exact answer in terms of e.) In 1995, the rate of growth of Internet users in the country is million per year. (Type an integer or decimal rounded to one decimal place as needed.) (c) The number of Internet users in the country in 2000 is about million (Type an integer or decimal rounded to one decimal place as needed.) In 2000, the rate of growth of Internet users in the country is million per year. Type an integer or decimal rounded to one decimal place as needed.) (d) The number of Internet users in the country in 2011 is million. (Type an integer or decimal rounded to one decimal place as needed.) In 2011, the rate of growth of Internet users in the country is million per year. (Type an integer or decimal rounded to one decimal place as needed.) (e) Choose the correct answer below. A. The rate of growth of the number of Internet users in the country decreases. B. The rate of growth of the number of Internet users in the country increases. C. The rate of growth of the number of Internet users in the country increases for a while and then decreases. OD. The rate of growth of the number of Internet users in the country decreases for a while and then increases