Given the amount function A (t) = t - 3t + 46, find the accumulation function a(t) at time t = 7. %3D
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- The formula for the amount A in an investmentaccount with a nominal interest rate r at any timet is given by A(t)=a(e)rt, where a is the amount ofprincipal initially deposited into an account thatcompounds continuously. Prove that the percentageof interest earned to principal at any time t can becalculated with the formula I(t)=ert1.The formula for an increasing population is given by p(t)=P0ert where P0 is the initial population and r0. Derive a general formula for the time t it takes for the population to increase by a factor of M .The population Pinmillions of Texas from 2001 through 2014 can be approximated by the model P=20.913e0.0184t, where t represents the year, with t=1 corresponding to 2001. According to this model, when will the population reach 32 million?
- Q3Initially, 100 milligrams of a radioactive substance were present. After 6 hours the mass had decreased by 3%. If the rateof decay is proportional to the amount of the substance present at time t, find the amount remaining after 24 hours.A 200-gal tank is half full of distilled water. At time t = 0, a solution containing 0.5 lb /gal of concentrate en-ters the tank at the rate of 5 gal/ min, and the well-stirred mixture is withdrawn at the rate of 3 gal/min. a. At what time will the tank be full? b. At the time the tank is full, how many pounds of concentrate will it contain?What is the amount of salt in the tank at time t = 0?
- Consider 250g of iodine which decomposes at a rate proportional to the amount present. Around 150g of iodine decomposes in 10.5754 days. What is the proportionality constant k? 0.0483032/day None -0.0483032/day -0.0866436/day 0.0866436/dayDetermine the AV at time 9 of $100 invested at time 4 given the accumulation function a(t)=0.05t2+1.A 200-gal tank is half full of distilled water. At what time (t) = 0, a solution containing 0.5 lb/gal of concentrate enters the tank at the rate of 5 gal/min, and the well-stirred mixture is withdrawn at the rate of 3 gal/min. a. At what time will the tank be full? b. At the time the tank is full, how many pounds of concentrate will it contain?
- The radioactive element polonium decays according to the law given below where Q0 is the initial amount and the time t is measured in days. Q(t) = Q0 · 2−(t/140) If the amount of polonium left after 280 days is 90 mg, what was the initial amount present?where p(t) is the proportion of the population that knows the rumor at time t and a and k are positive constants. (a) When would half the population have heard the rumor? (b) When is the rate of spread of the rumor greatest?A.) use a right hand sum with three rectangles to estimate the net change in population between t=1 and t=7 B.) how would you visualize the exact net change in population between t=1 and t=7? C.) was the population larger at time t=1 or time t=7? How do you know?
