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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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- 21. 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_forward14) The total health expenditure per capita is modeled by H(1) 67e00 where f is the number of years. The predicted health expenditures (in dollar) after 13 years isarrow_forwardIf f (6) = -3, f’(6) = 6, g(6) = -1, and g’(6) = -4, determine (??/?−?)′(6).arrow_forward
- 1. A room with a volume of 5000 ft3 is full of air which contains 2% (CO). Pure air containing no (CO) is pumped into the room at the rate of 200 cubic feet per minute, and the well-mixed air is vented from the room at the same rate. a. Find the equation that models the amount of (CO), x(t), in ft3, which is in the room, as a function of time. b. How long will it take for the concentration of (CO) in the room to reach 0.01%?arrow_forward1 2.if (fT))= , find f f(4t)arrow_forwardQ1. If the growth rate of the number of virus infection at any time t is proportional to the number of infected people present at t and doubles in 1 week, how many people can be expected to be infected after 2 weeks? After 10 weeks? Assume the number of people infected by a virus at time t = 0 is 50.arrow_forward
- 3. limx-10 Vx – 1arrow_forwardSuppose that when a certain lake is stocked with fish, the birth and death rates B and 8 are both inversely propor- tional to P. (a) Show that P() = (4kt + /Po)´. where k is a constant. (b) If Po = 100 and after 6 months there are 169 fish in the lake, how many will there be after 1 year?arrow_forwardProblem: After being built, a car must be painted. The revenue, R, in dollars, when x cars are painted can be modelled by the function R(x) = 1000x – 0.01x2. a) Determine the average rate of change of revenue when painting 20 to 50 cars. (3) b) Estimate the instantaneous rate of change of revenue after painting 50 cars. (3) c) Interpret the results found in parts a) and b). (2) Problem: After being built, a car must be painted. The revenue, R, in dollars, when x cars are painted can be modelled by the function R(x) = 1000x – 0.01x2. a) Determine the average rate of change of revenue when painting 20 to 50 cars. b) Estimate the instantaneous rate of change of revenue after painting 50 cars. c) Interpret the results found in parts a) and b).arrow_forward
- 4. The growth rate of a colony of ants is given by the formula 10t 2 (1+t²)² where t is measured in hours. If 100 ants are initially present then how many are present after 2 hours? The number of ants present after 2 hours isarrow_forward8. The rate of electric vehicle purchases in the US from 2012 to 2024 can be modeled using the following a. equation, where V(t) is measured in vehicles per year, and t is in years since 2012 (e.g. t = 0 in year 2012): = 3600t² + 11,000t + 59,300 V(t) How many more EVs were purchased in 2023 than in 2022? Report 3 significant figures. more EVs b. Determine the rate at which the number of electric vehicles being purchased each year is changing in the year 2024. Report 3 significant figures with appropriate units. 5arrow_forward2. From 2007 to 2014, there was a dramatic increase of smartphone sales. The number of smartphones (in millions) sold to end users from 2007 to 2014 is modeled by the function c(t) = 114.9e0.345t, where t represents the number of years after 2007. a. Find c'(t) b. Find c'(2), and write a sentence interpreting the meaning. Be sure to include units.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage