Find the time it takes for $9,100 to double when invested at an annual interest rate of 5%, compounded continuously. Find the time it takes for $910,000 to double when invested at an annual interest rate of 5%, compounded continuously. years The number of bacteria in a culture is given by the function n(t) = 91560'5' where t is measured in hours. (a) What is the continuous rate of growth of this bacterium population? % (b) What is the initial population of the culture? (c) How many bacteria will the culture contain at time t=5 hours? The half life of Sodium-24 is 14.96 hours. If a sample contains 160 mg, how many mg will remain after 110 hours? rm You go to the doctor and he gives you 10 milligrams of radioactive dye. After 24 minutes, 4.75 milligrams of dye remain in your system. To leave the doctor's office, you must pass through a radiation detector without sounding the alarm. Suppose the detector will sound the alarm if more than 2 milligrams of the dye are in your system. How long will your visit to the doctor take, assuming you were given the dye as soon as you arrived? Give your answer to the nearest minute. You will spend minutes at the doctor's office. Blood is a buffer solution. When carbon dioxide is absorbed into the bloodstream, it produces carbonic acid and lowers the pH. The body compensates by producing bicarbonate, a weak base to partially neutralize the acid. The equation which models blood pH in this situation is :13 pH(:.-:) = 6.1 + log( 800) where :3 is the partial pressure of carbon dioxide in arterial blood, measured in torr. Find the partial pressure of carbon dioxide in arterial blood if the pH is 7.7. i ] C1" In the above graph of y = f( x ), find the slope of the secant line through the points 1 -3, f{ -3 ) ) and ( 1, f( 1 J ). Ck In the above graph of y = f( x ), find the slope of the secant line through the points [ -1, f{ -1 ) ) and ( 3, f( 3 I ). The following table shows the daily receipts in millions of dollars of the movie "The Hunger Games" after its opening on 23 March 2012. Days SReceipts 0 152.535 14 33.111 28 14.666 42 5.587 56 2.95 70 1.567 84 0.852 98 0.397 112 0.279 126 0.518 Find the average rate of change of the daily receipts from day 0 to day 14. S millions f day 18 I6 I4 12 10 Estimate the instantaneous rate of change at z = 2 [:1 Your estimate needs to be within 1096 of the exact answer. For each value below, enter the number correct to four decimal places. Suppose an arrow is shot upward on the moon with a velocity of 48 mfs, then its height in meters after t seconds is given by Mt) = 48t 0.83132. Find the average velocity over the given time intervals. [3, 4]: [3, 3.5]: l ' [3, 3.1]: l ' [3, 3.01]: l ' [3, 3.001]: ' ' Estimate the instantaneous rate of change of t) = 49 4 at the point: t = 2 In other words, choose x-values that are getting closer and closer to 2 and compute the slope of the secant lines at each value. Then, use the trend I pattern you see to estimate the slope of the tangent line. :1 Your answer should be accurate to at least 2 decimal places. 5 Estimate the instantaneous rate of change of P(t) = at the point t = - 3 t+1 Your answer should be accurate to at least 3 decimal places.The following table shows the daily receipts in millions of dollars of the movie "Avatar" for successive Fridays after its opening on Friday 18 December 2009. Weeks SReceipts 3 50.306 6 31.28 9 16.24 12 6.526 15 0.98 18 0.92 21 0.335 24 0.076 27 0.044 Estimate the instantaneous rate of change of daily receipts 12 weeks after the opening day. Round to four decimal places. (1 Estimate the area between the x-axis and the graph of f (m) = 9 2:2 over the interval [0, 3] by using the three rectangles shown here