4. K-Mobile offers a monthly cellular plan for $39.99. It includes 350 anytime minutes plus $0.25 per minute for additional minutes. The following function is used to compute the monthly cost for a subscriber: C(x) 39.99 for 0350 ;where x is the number of anytime minutes used. [10 marks] ls C(x) continuous at x: 350? 5. Give that a Firm has a revenue function R(q) = l300q + 30g2 q3 from the sale of q units (kg) ofa certain product, dR (a) Find the marginal revenue function (Hint: find 07 ) 9 (b) What is the value of the marginal revenue when 30 items are sold'? What do you understand the answer to mean? 6. Ifthe Gross National Product (GNP) of Antigua (in millions of dollars) is described by the function: cu): 2t3+50t2+30t+8000 ;(0 St 5 l 1) ;where t = 0 corresponds to the beginning of 1999. (i ) At what rate was the GNPchangt'ng at the beginning of 2005 ? (ii) At what ratewastheGNPchanging atthebeginning of 2010? (ii i ) What was the average growth of the GNPover the period 2005 20 l 0 ? r mt 7. Compound interest: A = p (1 + E) Continuous Compound interest: A = Fe '1 ; where A= amount (future value) at the end oft years P= principal (present value) r = annual rate (expressed as a decimal) m = number of compounding periods per year t = time in years' (a) If $5,000 is invested in an account paying 9% compounded monthly, How much will be in the account at the end of 5 years? Compute the Answer to the nearest cent. (b) If $5,000 is invested in an account paying 9% compounded continuously, How much will be in the account at the end of 5 years? Compute the Answer to the nearest cent. September , 2023 ANTIGUA & BARBUDA INTERNATIONAL INSTITUTE OF TECHNOLOGY FINAL EXAM CALCULUS FOR BUSINESS MATH201-01 Attempt all questions. 2 hour. 1. Find the following limits: (1) lim x*+6x +8 [5 marks] x-+0 2x3- 2x2 +9x (ii) lim x' - 6x + 7 [5 marks] x-0x +x-13 (iii) lim- x2 - 6x+7 [5 marks] xbox+x-13 (iv) lim- x- - 5x+6 [5 marks] x-2x +x-12 2. A major corporation is building a 4840-acre complex of homes, offices, stores, schools, and churches in the rural community of Friars Hill. As a result of this development, the planners have estimated that Friars Hill's population (in thousands) t years from now is given by: P (1 ) = = 25t~ + 125t+ 2000 12 + 5t+400 i. What is the current population of Friars Hill [5 marks] ii. What will be Friars Hill population in the long run (Hint: long run = Limit of P(t) as t tends to infinity) . [5 marks] 3. (a) For what value of Bisthe function f(x) = Bx for x 52 1/ x - 6 -8 for x > 2 [10 marks] continuous at x = 2? (b) Given the function f(x)= 2x-6 for x