22. The function fx)=log1, x has the point (10, 1) on its graph. Find the coordinates of the image point transformed from (10, 1) on the transformed function f(x)=21og1,5(x+ 4)-6. а. (-2, -4) b. (2, 5) с. (14, -5) d. (4, 5)
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- suppose that 50,000 bacteria are in a dish and that the population decays continuously by 4% per hour. what is a function that represents the population P as a function of time t (in hours). what will the population be after 4 hours and after 8 hours.When a breeding group of animals is introduced into a restricted area such as a wildlife reserve, the population can be expected to grow rapidly at first but to level out when the population grows to near the maximum that the environment can support. Such growth is known as logistic population growth, and ecologists sometimes use a formula to describe it. The number N of deer present at time t (measured in years since the herd was introduced) on a certain wildlife reserve has been determined by ecologists to be given by the function below. (Round your answers down to the nearest whole number.) N = 12.35 0.01 + 0.54t (a) How many deer were initially on the reserve? deer(b) Calculate N(12).N(12) = deer (c) Express the number of deer present after 17 years using functional notation. N Calculate the number of deer present after 17 years. deer(d) How much increase in the deer population do you expect from the 12th to the 17th year? deerWhen a breeding group of animals is introduced into a restricted area such as a wildlife reserve, the population can be expected to grow rapidly at first but to level out when the population grows to near the maximum that the environment can support. Such growth is known as logistic population growth, and ecologists sometimes use a formula to describe it. The number N of deer present at time t (measured in years since the herd was introduced) on a certain wildlife reserve has been determined by ecologists to be given by the function below. (Round your answers down to the nearest whole number.) N = 12.33 0.01 + 0.54t (a) How many deer were initially on the reserve? deer(b) Calculate N(12).N(12) = deer(c) Express the number of deer present after 17 years using functional notation. N Calculate the number of deer present after 17 years. deer(d) How much increase in the deer population do you expect from the 12th to the 17th year? deer
- sketch the graph of f(x) =1 log2 (x+3) state vertical shift, horizontal shift, ordered pair where (1,0) transforms to, equation of asmypotote.Suppose that a population grows according to a logistic model with carrying capacity 6500 and k = 0.0015 per year. If the initial population is 1000, write a formula for the population after t years.Suppose that a particular pond can sustain up to 30,000 tilapia and that the undisturbed population of tilapia in this environment can be modeled according to the logistic model as dP/dt = 4(1 - P/30,000)P. Suppose that the farmer wishes to sell 15,000 fish per year. In this case, the harvest model will be constant. a. Following the constant harvest model, write an equation, involving a derivative, that governs the population of tilapia. b. What happens to the population if P = 5000? c. What happens to the population if P = 20,000? d. Find the two equilibria for this model.
- Suppose two students are memorizing the elements on a list according to the rate of change equation: dL/dt = 0.5(1-L). L represents the fraction of the list that is memorized at any time t. (a) If one of the students knows one-third of the list at time t = 0 and the other student knows none of the list, which student is learning most rapidly at this instant? Why? (b) What does the rate of change equation predict for someone who begins with the list completely memorized? Explain.If $4000 is invested at 7.3% compounded continuously, graph the amount in the account as a function of time for a period of 9 years. Choose the correct graph. A. 024681002000400060008000tA A coordinate system has a horizontal t-axis labeled from 0 to 10 in increments of 1 and a vertical A-axis labeled from 0 to 8000 in increments of 1000. A line segment starts at (0, 4000), passes through (2, 4700), and ends at (9, 6900). All coordinates are approximate. B. 024681002000400060008000tA A coordinate system has a horizontal t-axis labeled from 0 to 10 in increments of 1 and a vertical A-axis labeled from 0 to 8000 in increments of 1000. A line rises from left to right passing through the points (0, 0), and (1, 4300). All coordinates are approximate. C. 024681002000400060008000tA A coordinate system has a horizontal t-axis labeled from 0 to 10 in increments of 1 and a vertical A-axis…The amount of plutonium remaining from 1 kilogram after x years is given by the function W(x)=2^-x/24,360 Estimate how long it will take for the 1 kilogram to decay to half its original weight.
- Suppose a new screening tool is developed for prostate cancer in men with much higher sensitivity and specificity as the PSA test. Let X be the distribution of scores resulting from that test in men aged 45-65. Suppose after a log transformation, X~N(-0.25, 0.76). What is the range of scores that results in the top and bottom 2.5% of scores for this test?When time is measured in days, the decay constant for a particular radioactive isotope is 0.16. Determine the time required for a confined sample of the isotope to fall to 45% of its original value. The time required for a confined sample of the isotope to fall to 45% of its original value is about __________________days.in the early 1970s there were approximately 40,000 trees lining the streets of Newton. Today, that number is about 26,000-a 35% loss. The current annual rate of decline is about 650 trees per year. At this rate, if unchecked, public street trees would diminish to approximately 10,000 within a generation (25 years), and in 40 years, public street trees would no longer be part of the Newton landscape. a) show work for how that loss comes to be 35% b) show work for how it comes to be a decline of 650 trees per year