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In Problems 1–8, express the relationship between f′(x) and f(x) in words, and write a differential equation that f(x) satisfies. For example, the derivative of f(x) = e3x is 3 times f(x);y′ = 3y. (If necessary, review Section 3.4).
2. f(x) = e−2x
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Chapter 5 Solutions
Pearson eText for Calculus for Business, Economics, Life Sciences, and Social Sciences, Brief Version -- Instant Access (Pearson+)
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- Section 5.1 is specifically focusing on antiderivatives. As the graph shown is f'(x), I am assuming I need to find the formula (equation) of the graph in order to find f(x) and answer questions (a)-(e). I am having a difficult time discovering this formula (equation) and understanding if I am even approaching this problem correctly. Please help! Thank you.arrow_forwardFor each dif erential equation in Problems 1–21, find the general solutionby finding the homogeneous solution and a particular solution. Please DO NOT YOU THE PI method where 1/f(r) * x. Dont do that. Instead do this, assume for yp = to something, do the 1 and 2 derivative of it and then plug it in the equation to find the answer.arrow_forward1. (MG 9, Section 6 Purple). For each of the following, express the equation in exponential form. (a) In4 = x is equivalent to eA = B with A = and B = (b) Inx= 3 is equivalent to eC = D with C = and D =arrow_forward
- + I/ MI * 00 Energy consumption in a particular country in quadrillion BTUS can be modeled by C(x) = - 0.014x + 1.295x+ 68,958, where x is the number of years after 1970. a. One solution to the equation 89.258 = - 0.014x+ 1.295x+68.958 is x = 20. What does this mean? b. Graphically verify that x 20 is a solution to 89.258 = - 0.014x+1.295x + 68.958. c. To find when after 2020 the energy consumption in that country will be 89.258 quadrillion BTUS according to the model, is there a need to find the second solution to this equation? Why or why not? a. Choose the correct answer below. O A. In 1990, consumption was 68.958 quadrillion BTUS. O B. In 2020, consumption was 68.958 quadrillion BTUS. O C. In 1990, consumption was 89.258 quadrillion BTUS. O D. In 2020, consumption was 89.258 quadrillion BTUS. Click to select your answer and then click Check Answer. parts 2. remaining Clear All Check Answer P Pearson &17 PM ere to search 近 1202/LL/Z PrtSc F11 F12 F10 sup F7 F8 & Backspace 23 3. i 5.…arrow_forward1.) (Sections 4.1 & 4.2) A virus is spreading through a population, with 8% more people actively infected every 10 days. Initially there were 102 people actively infected. (a) Find an exponential model of the form V(t) = Ab' that will compute the number of people actively infected V as a function of t in days. (b) What is the per-day rate of infection? Give as a percentage accurate to two decimal places (1.23% per day, for example). (c) What is the doubling time for infections? That is, how long until twice as many people are infected than initially? Give accurate to the nearest integer and label appropriately.arrow_forwardQuestion 3 Given h(x) = (-x² - 2x - 2)³, find h' (0).arrow_forward
- Model the following data using an exponential function of the form f(x) = Ab". You need to do this rigorously, that is, set up a system of equations, and solve it to get A and b. Getting the right answer by guessing will earn no credit. (a) f(x) is exponential and goes through the points (1, 2) and (4,6). (b) f(x) is exponential and goes through the points (2, 75) and (5, 9375).arrow_forwardSolve. a) ln(x+1) + ln(x-1) = 0 b) e8-5x = 16 c) ln(2x) - ln4 = 3 d) 2ln(x+3) = ln(12x)arrow_forwardExample 35. 3 y = (x + Væ)'arrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,
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