2. The price p {in dollars] and the quantitv it sold of a NEW smartphone obey the demand equation p = x + 1000. {10 points] la] Find a model that expresses the revenue R as a function of x. ibi IWhat is the revenue 0400 units are sold? it] What quantity x of the new smartphone maximizes the revenue? id} What is the maximum revenue? to] What price should the smartphone company charge to maximize revenue. 4. A rare species of insect was discovered in the Amazon Rain Forest. To protect the species, environmentalists declared the insect endangered and transplanted the insect into a protected area. The population P of the insect t months after being transplanted is (10 points) 50(1 + 0.5t) P(t) = 2 + 0.01t (a) How many insects were discovered? In other words, what was the population when t = 0? (b) What will the population be after 5 years? (c) Use the graph of P and the algebraic concept of the horizontal asymptote. Determine the end behavior of P. What is the largest population that the protected area can sustain? 2000 1000 1000 2000 3000 4030 5060 6030 7000 8009 6000 55. Algebraically, find the domain of the function, find the horizontal, vertical, and/or oblique asymptotes. (10 points) 9(x) - 2X - 14x + 24 x2+ 6x - 40 (a) Domain: (b) Horizontal Asymptotes: (c) Vertical Asymptotes: (d) Oblique Asymptotes: Use the graph below to check your answer. 10 (3, 0) (0, -0.6) 63. For the polynomial function HI) = 2x3 + 5x2 28x 15, determine the foiiowlng: (10 points] la] The maximum number of reai zeros the function may have: lb} List the potential rational zeros based on the Rational zero Theorem. The national Zero Theorem states that, if the polynomial jI"(Jr::l = our\" + on_1x"" + + nix + on has Integer coefficients, then every rational zero of flier) has the form 5 where o is a factor of the constant term on and o is factor of the leading coefficient on. Potential Rational zeros: it) Based on the grep h, determine the real zeros of MI). Real Zeros: _ , (d) Factor k(x) completely over the real numbers. Factored Form of k(x) = (e) Find the x-intercepts. x-intercepts: (f) Find the y-intercept. y-intercept:6. Find the x- and y-intercepts of the function f(x) = (4x - 1)2(x + 3). (10 points) x-intercepts y-intercepts 7Directions: Answer each question as best as you can. Show all your thinking with the correct answer to get full credit on each question. Be sure to use correct mathematical notation. form. and units as demonstrated in the class or in videos. 1. You are moving out of your parent's house into a new apartment, and you need to rent a truck to help you with your move. 'i'ou have found a truck rental store which charges $129.50 to rent the vehicle plus SCLlS per mile that you drive the vehicle. (it) points) la] Find a linear model that expresses the mat 35 a function of miles driven m. {b} If you only have 5140 to spend on the rental truck, howr many miles can you drive the truck? (:1 The drive to your new apartment will be a total of 16 miles round trip. Find the rental cost if 15 miles are driven