4- (a) X' = In the following problems solve the given initial value problem. HIN 2 — X X(0) = (²³)
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- If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per second. What is the terminal velocity, and how long does it take the filter to reach 99 of terminal velocity? Use a table increment of 0.1 and given your answer to the nearest tenth of a second.Cesium-137 has a half-life of about 30 years. If we begin with 200 mg of cesium-137, will it take more or less than 230 years until only 1 milligram remains?Suppose P(x) represents the profit on the sale of x Blu-ray discs. If P(1,000) = 4,000 and P'(1,000) = −1, what do these values tell you about the profit? P(1,000) represents the profit on the sale of? Blu-ray discs. P(1,000) = 4,000, so the profit on the sale of? Blu-ray discs is $? P'(x) represents the rate of change of the profit marginal revenue profit marginal cost as a function of x. P'(1,000) = −1, so the profit is decreasing at the rate of $ ? per additional Blu-ray disc sold.
- The number of units of weekly output of a certain product is represented by the equation shown below, where x is the number of workers on the assembly line. There are presently 72 workers on the line. Q(x) = 200x + 8x² (a) Find Q'(x) and estimate the change in the weekly output caused by the addition of one worker. (b) Calculate Q(73) – Q(72) to see the actual change in the weekly output. -The registrar of Kellogg University estimates that the student enrollment in the Continuing Education division will grow at the rate of N'(t) = 2500(1 + 0.2t)-3/2 students/year, t years from now. If the current student enrollment is 1000, find an expression giving the enrollment t years from now. N(t) = What will be the enrollment 5 years from now? (Round your answer to the nearest student.) studentsIf h(x)=2-4/3x given the equation for h-1(x)
- When they invest K dollars, a fishery can produce Q(K) pounds of fish per month, where Q(K) = 104 K/3. In t months from now, their total investment will be K(t)=0.5t2+300 t +515 dollars. At what rate is the production of fish changing with respect to time 8 months from now? In 8 months from now, the fisher's production will be increasing at a rate of 51 pounds per month-4 x' Solve x(0) = 2Suppose P(x) represents the profit on the sale of x Blu-ray discs. If P(1,000) = 8,000 and P'(1,000) = -6, what do these values tell you about the profit? P(1,000) represents the profit on the sale of Blu-ray discs. P(1,000) = 8,000, so the profit on the sale of Blu-ray discs is $ . P'(x) represents the rate of change of the profit as a function of x. P'(1,000) = -6, so the profit is decreasing at the rate of $ per additional Blu-ray disc sold.
- (3) A production manager determines that t months after production on a new product begins, the number of units produced will be N thousand, where N(t)=(〖17t〗^2+13t)/((2t+1)^2 )(i) What would be the level of production 5 months into operations.(ii) What would be the level of production be in the long runSuppose P(x) represents the profit on the sale of x Blu-ray discs. If P(1,000) = 1,000 and P'(1,000) = −7, what do these values tell you about the profit? P(1,000) represents the profit on the sale of Blu-ray discs. P(1,000) = 1,000, so the profit on the sale of Blu-ray discs is $ . P'(x) represents the ---------------Select--------------- rate of change of the profit profit marginal cost marginal revenue as a function of x. P'(1,000) = −7, so the profit is decreasing at the rate of $ per additional Blu-ray disc sold.12. If $5000 is deposited in a bank paying r% interest (r = interest rate), the amount 3 years later will be given by A(r) = 5000 (1 + 0.01r)³ Find A'(5) and interpret the answer.
