Q1

Students in a zoology class took a final exam. They took equivalent forms of the exam at monthly intervals thereafter. After t months, the average score S(t), as a percentage, was found to be given by the following equation, where t2 0. Complete parts (a) through (e) below. S(t) = 76 - 16 In (t + 1), Osts80 a) What was the average score when they initially took the test? The average score was %. (Round to one decimal place as needed.) b) What was the average score after 4 months? The average score after 4 months was |%. (Round to one decimal place as needed.) c) What was the average score after 24 months? The average score after 24 months was |%. (Round to one decimal place as needed.) d) Find S'(t). s'(t) =0 e) Find S'(4) and S'(24), and interpret the meaning of these numbers. s'(4) = , which means that after 4 months, the average score is by points a month and S'(24) = ], which means that after 24 months, the average score is by points a month. (Type integers or decimals.) decreasing increasingThe profit, in thousands of dollars, from the sale of x thousand candles can be estimated by P(x) = 3x - 0.3x In x. Complete parts (a) through (c). a) Find the marginal profit, P'(x). P'(x) = b) Find P'(619), and explain what this number represents. P'(619) = (Type an integer or decimal rounded to the nearest thousandth as needed.) What does P'(619) represent? O A. The additional cost, in thousands of dollars, to produce a thousand candles once 619,000 candles have already been sold. O B. The additional profit, in thousands of dollars, when 619,000 candles are sold. O C. The additional cost, in thousands of dollars, to produce 619,000 candles. O D. The additional profit, in thousands of dollars, for selling a thousand candles once 619,000 candles have already been sold. c) How many thousands of candles should be sold to maximize profit? (Type an integer or decimal rounded to the nearest thousandth as needed.)The number of liver transplants perlormed in a particular country in year x is approximated by x) = 241.3 + 2306 In x where x 2 5 and x=5 corresponds to the year 1995. a) Estimate the number of transplants in 2022. b] Find ((321. a) According to this model. there should be approximately liver transplants in 2022. (Round to the nearest integer as needed.) b] f'(32}= I: per year (Round to the nearest integer as needed.)