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A: Solution
The dropdwons that say "select" on part c and d is asking "is it increasing, decreasing or staying constant"
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- According to the solution in Exercise 58 of the differential equation for Newtons law of cooling, what happens to the temperature of an object after it has been in a surrounding medium with constant temperature for a long period of time? How well does this agree with reality?Explain the difference between the average rate of change of y as x changes a to b, and the instantaneous rate of change of y at x=aThe rate of change of the value of goods exported from a country between 1990 and 2001 can be modeled as E'(t) = -1.662t² + 16.474t + 7.632 billion dollars per year and the rate of change of the value of good imported into the country during those years can be modeled as I'(t) = 4.916t + 40.861 billion dollars per year where t is the number of years since 1990. (a) Calculate the difference between the accumulated value of imports and the accumulated value of exports from the end of 1990 through 2001. (Round your answer to three decimal places.) $ billion (b) Is the answer from part (a) the same as the area of the region(s) between the graphs of E' and I'? Yes No Explain. Since the graphs ---Select--- , the answer to part (a) ---Select--- the area of the region(s) between the curves.
- A population of 400 bacteria is introduced into a culture and grows in number according to the equation below, where t is measured in hours. P(t) = 400(2 4t 56 + t² Find P'(t). P'(t) = + bacteria/hour Find the rate at which the population is growing when t = 2. (Round your answer to two decimal places.) P'(2) = bacteria/hourFind the rate of change of the reciprocal function f(x): with respect to x when x = 19, 20, and 21. (Use symbolic notation and fractions where needed.) f'(19) = f'(20) = f'(21) =The concentration of a certain drug in a patient's bloodstream t hr after injection is given by the following function. c(t)=0.2t/t^2+9 (a) Find the rate (in percent/hr) at which the concentration of the drug is changing with repect of time. C'(t)= (b) How fast (in percent/hr) is the concentration changing 1/2 hr,3 hr, and 10 hr after the injection? (round your answers to four decimal places.)
- A population of 450 bacteria is introduced into a culture and grows in number according to the equation below, where t is measured in hours. =450(5. 5+ Find P'(t). P'(t) = P(t) = 4t 73 + t². bacteria/hour Find the rate at which the population is growing when t = 4. (Round your answer to two decimal places.) P'(4) = bacteria/hourA population of 450 bacteria is introduced into a culture and grows in number according to the equation below, where t is measured in hours. Find the rate at which the population is growing when t = 5. (Round your answer to two decimal places.) P(t)=450(1+5t/62+t^2) P'(5)= bacteria/hourThe amount of photosynthesis that takes place in a certain plant depends on the intensity of light x according to the equation f(x) = 125x2 − 15x3. (a) Find the rate of change of photosynthesis with respect to the intensity of light.f '(x) = (b) What is the rate of change when x = 1? When x = 3? when x = 1 when x = 3 (c) How fast is the rate found in part (a) changing when x = 1? When x = 3? when x = 1 when x = 3