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- WaterWater flows into a tank, and a certain part of it drains out through a valve. The volume v in cubic feet of water in the tank at time t satisfies the equation dvdt=5(v/3). If the process continues for a long time, how much water will be in the tank?Differentaiate the function. h(x)=ln(x+√x2-12)Strontium 90 (Sr-90), a radioactive isotope of strontium, is present in the fallout resulting from nuclear explosions. It is especially hazardous to animal life, including humans, because, upon ingestion of contaminated food, it is absorbed into the bone structure. Its half-life is 27 years. Find the function Q(t)that expresses the amount of Sr-90 present at time t, where Q0is the amount present initially and t is measured in years. Q(t) = If the amount of Sr-90 in a certain area is found to be 16 times the "safe" level, find how much time (in years) must elapse before the safe level is reached. Olivia plans to secure a 5-year balloon mortgage of $250,000 toward the purchase of a condominium. Her monthly payment for the 5 years is calculated on the basis of a 30-year conventional mortgage at the rate of 5%/year compounded monthly. At the end of the 5 years, Olivia is required to pay the balance owed (the "balloon" payment). What will be her monthly payment for…
- Certain pieces of antique furniture increased very rapidly in price in the 1970s and 1980s. For example, the value of a particular rocking chair is well approximated by V=70(1.2)^t, where VV is in dollars and tt is the number of years since 1975. At time t, what is the rate at which the price is increasing? rate =A colony of bacteria grows according to the law of uninhabited growth. The growth is modeled by the function N(t)=48e^0.375t where N is measured in grams and t is measured in days. How long will it take for the population to reach 2970 grams?If R denotes the reaction of the body to some stimulus of strength x, the \ sensitivity S is defined to be the rate of change of the reaction with respect to x. A particular example is that when the brightness x of a light source is increased, the eye reacts by decreasing the area RR of the pupil. The experimental formula R=37+21x4/1+0.3x4 can be used to model the dependence of R on x when R is measured in square millimeters and x is measured in appropriate units of brightness. Find the sensitivity corresponding to x=2x=2. Sensitivity = ?
- The intensity of a sound is given by I(L)=I010.1L where L is loudness of the sound measured in decibels and I0 is the minimum intensity detectable by the human ear. What is d2/dL2[I(L)] in terms of the function itself, i.e./ I(L)? (ln100/100)I(L) (ln10)2/100 I(L) .01/(ln10)2 I(L) .01/ln10 I(L)Hydrocodone bitartrate is used as a cough suppressant. After the drug is fully absorbed, the quantity of drug in the body decreases at a rate proportional to the amount left in the body, with constant of proportionality k. Suppose that the half-life of hydrocodone bitartrate in the body is 3.6 hours, and that the oral dose taken is 11 mg.Exponential function f(x) = a(b)^x, where 0< b < 1, represents a decreasing function. True or false and how?
- Radioactive carbon-14 decays according to the function Q(t)=Q0e−0.000121t where t is time in years, Q(t) is the quantity remaining at time t, and Q0 is the amount of present at time t = 0. Estimate the age of a skull if 23% of the original quantity of carbon-14 remains.After an alcoholic beverage is consumed, the concentration of alcohol in the bloodstream (blood alcohol concentration, or BAC) surges as the alcohol is absorbed, followed by a gradual decline as the alcohol is metabolized. The function C(t) = 0.135te−2.802t † models the average BAC, measured in g/dL, of a group of eight male subjects, t hours after rapid consumption of 15 mL of ethanol (corresponding to one alcoholic drink). What is the maximum average BAC (in g/dL) during the first 4 hours? (Round your answer to three decimal places.) g/dL After how many hours does it occur? (Round your answer to two decimal places.) hAfter an alcoholic beverage is consumed, the concentration of alcohol in the bloodstream (blood alcohol concentration, or BAC) surges as the alcohol is absorbed, followed by a gradual decline as the alcohol is metabolized. The function C(t) = 0.135te−2.802t † models the average BAC, measured in g/dL, of a group of eight male subjects, t hours after rapid consumption of 15 mL of ethanol (corresponding to one alcoholic drink). What is the maximum average BAC (in g/dL) during the first 4 hours? (Round your answer to three decimal places.) After how many hours does it occur? (Round your answer to two decimal places.)
