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- If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per second. What is the terminal velocity, and how long does it take the filter to reach 99 of terminal velocity? Use a table increment of 0.1 and given your answer to the nearest tenth of a second.Does the equation y=2.294e0.654t representcontinuous growth, continuous decay, or neither?Explain.The kinetic energy E of an object varies jointly with the object’s mass m and the square of the object’s velocity v . An object with a mass of 50 kilograms traveling at 16 meters per second has a kinetic energy of 6400 joules. What is the kinetic energy of an object with a mass of 70 kilograms traveling at 20 meters per second?
- 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.Find the constant of proportionality. y is directly proportional to x. If x=30, then y=15.Find the unknown value. 27. y varies jointly with x and the cube root of 2. If when x=2 and z=27,y=12, find y if x=5 and z=8.
- When a certain drug is taken orally, the concentration of the drug in the patient's bloodstream After t minutes is given by C(t)=0.06t0.0002t2 where 0t240 and concentration is measured in mg/L .When is the maximum serum concentration reached, and what is that maximum concentration?(b) Find the differential for y = -5 %3DOn a monthly basis, when a factory employs L worker-hours of labor, they can produce Q(L) = 7L + 40L/6 scooters. An investment in labor of K dollars gives them an employment level of L(K)=0.055K – 12,500 K worker-hours. The factory currently invests 2,000 dollars in labor. At what rate is the number of scooters being produced changing with respect to the amount they invest in labor? Round your final answer to 2 decimal places and include units with your answer. а.
- UCLAium-1919 is a radioactive element with a half-life of 140 days. Suppose that 10 mg of the element are placed in a lead container. Let y(t) represent the number of mg present t days later. Give exact answers only for all parts. No decimals, no rounding. The equation that represents the number of mg present t days later is y(t) = How many mg will be present after 10 weeks? Answer = In how many days will it take for 70% of the original sample to decay? Answer =The projected population of the United States for the years 2025 through 2055 can be modeled by P = 307.58e0.0052t, where P is the population (in millions) and t is the time (in years), with t = 25 corresponding to 2025.A shallow reservoir has a one-square-kilometer water surface and an average water depth of 2 meters. Initially it is filled with fresh water, but at time t=0 water contaminated with a liquid pollutant begins flowing into the reservoir at the rate of 400 thousand cubic meters per month. The well-mixed water in the reservoir flows out at the same rate. Your first task is to find the amount x(t) of pollutant (in millions of liters) in the reservoir after t months. The incoming water has a pollutant concentration of c(t) = 20 liters per cubic meter (L/m³). Verify that the graph of x(t) resembles the steadily rising curve shown here, which approaches asymptotically the graph of the equilibrium solution x(t) = 40 that corresponds to the reservoir's long-term pollutant content. How long does it take the pollutant content in the reservoir to reach 10 million liters? x(t) = 40- 30- 20- 10- 0 10 20 t
