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Response to adrenalin Experimental evidence suggests that the response y of the body to the concentration x of injected adrenalin is given by
(a) Is this function continuous for all x?
(b) On the basis of your conclusion in part (a) and the fact that in the context of the application
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- Decay of Litter Litter such as leaves falls to the forest floor, where the action of insects and bacteria initiates the decay process. Let A be the amount of litter present, in grams per square meter, as a function of time t in years. If the litter falls at a constant rate of L grams per square meter per year, and if it decays at a constant proportional rate of k per year, then the limiting value of A is R=L/k. For this exercise and the next, we suppose that at time t=0, the forest floor is clear of litter. a. If D is the difference between the limiting value and A, so that D=RA, then D is an exponential function of time. Find the initial value of D in terms of R. b. The yearly decay factor for D is ek. Find a formula for D in term of R and k. Reminder:(ab)c=abc. c. Explain why A=RRekt.arrow_forwardThe 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.arrow_forwardOMANTEL 96 B/s O * Oa“|23% | 12:20 PM chegg.com/homework-help 1 and answers / Prove That The Following Functions... Question: Prove That The Following Functions Are Well Defined: (a) The Function F: ... Please explain all of the steps used please. Prove that the following functions are well defined: (a) the function f: Z4 → Z12 given by f(x) = [3x] (b) the function f: Z, → Z1, given by fF) = [7x] Show transcribed image text Expert Answer o 100% (1 rating) This problem has been solved! See the answerarrow_forward
- 51arrow_forwardPlease answer the question below thank you.arrow_forwardConsider a revenue function defined as Provide your answer below: R(x) = At what value of x is the rate of change of revenue at production level x equal to zero? Give your answer as a decimal to one decimal place. Hint: You may wish to make use of the fact that for functions u = u(x), v = v(x) vu' - uv (²) == where u' and v' denote derivatives of u and v with respect to x. Content attribution d 200e0.4x 1 + x dx FEEDBACKarrow_forward
- 1. Consider the error function, erf(x), defined by erf(z) = . ´dt. e This function is important in probability and statistics. (a) Sketch the graph y = e=x². (b) Determine the intervals of decrease and/or increase of erf(r). (Hint: what is the derivative of erf(r)?) (c) Find erf(VT). [Hint: Apply the second Fundamental Theorem of Calculus (FTC) dx and the chain rule.] 2. In this problem we will see how to use Riemann Sums to calculate In(2). (a) According to the Fundamental Theorem of Calculus which bound b is needed to get | Edr = In(2)? Show your work. (b) Draw the rectangular figure corresponding to a left endpoint Riemann sum with n = 5 rectangles with equal bases. Is this an over or an under estimate? y = = 1 2 (c) Give a clear explanation of how to estimate/calculate In(2) to within an accuracy of ɛ, for example, e = 0.01. Specifically how many subdivisions are needed? (d) With n = 5 compare the left endpoint approximation L5, the right endpoint approximation R5 and their average…arrow_forward2/5 (0) M234n 16. 4. 7. 6. 4. 4. 3. 13 14 II 3. 12. 9. 7. 3. 14 3. 91 27 12 2. 91 2. a) - 91 7. 2. 2. (x) X (x)/ X (C) (x)/ (v) derivative. Which of the following could be a table of values for f? For all x in the closed interval [2, 5], the function f has a positive first derivative and a negative second Question 6 OE OB O A त (E) nonexistent () 1. (B) 3 2. If f (x) = In(x+ 4 +e*), then f'(0) is Question 5 O B Spotify- Liked Songs In in to your acco... New Tab ses/8372/quizzes/438817/take VQuiz: Lesson 42 Quiz pard | Richlands Higharrow_forward30- 27 24 21 18- 15 12 I 10 6 3 -3 -2 3 For the above function f( x ) = 4 - 0.6*, estimate ƒ'(x) using h = 0.001 for the following three values. ƒ'(-3.5) = ƒ'(0.75) = f'(2.25) =arrow_forward
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