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In Problems 30–35, the length of a plant, L, is a function of its mass, M, so L = f(M). A unit increase in a plant’s mass stretches the plant’s length more when the plant is small, and less when the plant is large. Assuming M > 0, decide if
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Calculus: Single And Multivariable
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- 2. Theorem LF = LD = G 63 Earrow_forward3. In 2008, the University of Central Florida was the sixth largest university in the country. The number of students can be modeled by the function f(t) = 50,000/( 1 + 5e012), where t is the time in years and t = 0 corresponds to 1970. (a) How many students attended UCF in 1990? (b) How many students attended UCG in 2000? (c) What is the carrying capacity of the UCF main campus?arrow_forwardIf the growth rate of the number of bacteria at any time t is proportional to the number present at t and doubles in 1 week, how many bacteria can be expected after 2 weeks?arrow_forward
- 1. Assume that the rate at which a hot body cools is proportional to the difference in temperature between it and its surroundings (Newton's law of cooling). A body is heated to 100°C and placed in air at 10°C. After 1 hour its temperature is 60°C. How much additional time is required for it to cool to 30°C?arrow_forward21. Suppose the number of users for a new social media app increases according to y = Yoe0.1t where y is measured in millions and t is measured in weeks. How long will it take for the number of users to triple? (a) In(30) weeks (b) 10 In(3) weeks (c) 10 In(3yo) weeks (d) 0.1 In(3) weeks (e) 3 In(1.1) weeksarrow_forward5. Consider a scenario in which a 20ft tall lamppost lights up a street. A 5ft tall woman stands close to the lamppost and the lamppost casts (a) her shadow on the ground in front of her. If she walks away from the lamppost at, a constant speed of 2ft/s, how quickly will the length of her shadow change? (b) ( ). Now suppose two people, one shorter than the other, walk away from the lamppost at the same constant speed v. Whose shadow is increasing faster, the taller person's or the shorter person's?arrow_forward
- Suppose that an accelerating car goes from 0 mph to 58.6 mph in five seconds. Its velocity is given in the following table, converted from miles per hour to feet per second, so that all time measurements are in seconds. (Note: 1 mph is 22/15 ft/sec.) Find the average acceleration of the car over each of the first two seconds. 4 5 t (s) 0 1 2 3 v(t) (ft/s) 0.00 29.32 50.82 66.4578.1886.00 average acceleration over the first second = help (units) average acceleration over the second second = help (units)arrow_forward4. ). Suppose that antibiotics are injected into a patient to treat a sinus infec- tion. The antibiotics circulate in the blood, slowly diffusing into the sinus cavity while simultaneously being filtered out of the blood by the liver. The following is a model for the concentration (in ug/mL) of the antibiotic in the sinus cavity as a function of time (in hours) since the injection. -at e e-Bt C(t) = B-a where a andB are constants with B > a > 0. ). Using the first derivative test, find when the maximum concentration occurs. (Your argument must use the first derivative test.) When does the rate of change of concentration begin to increase? (Your answer should be supported by a rigorous argument.)arrow_forward3. A rocket weighs 2000 tons at liftoff and burns fuel at a rate of 10 tons/minute. Express the rocket's weight W(in tons) as a function of the time t (in minutes) after liftoff.arrow_forward
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- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage