Use these formulas to express the numbers in terms of natural logarithms. 61. sinh-' (-5/12) 63. tanh (-1/2) 65. sech (3/5) Exercises 61–66 in 62. cosh¯' (5/3) 64. coth¯'(5/4) 66. csch'(-1/V3)
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- find the equation of the tangent line to the graph of the logarithmic function at the point (1,0) y=lnx3Suppose 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.Find and sketch an exponential equation of the form y = Cekx that passes through the points (0, 8) and (3, 4). Also calculate its derivative and indefinite integral.
- 5th derivative of y = log x^5 to the base 24 )Use logarithmic to creation to find the derivative of why with respect to theata 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? deer
- 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 = 12.33 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? deerState the derivative rule for the logarithmic function ƒ(x) = logb x.How does it differ from the derivative formula for ln x?Interest is compounded continuously at 5%. How long until a $5000 investment grows to $12000?
- Find the nth order derivative of the natural logarithm function y=lnx.Create a function in VBA of the equation of exponential curve fitting of The Annual Revenues of Singapore Post Company (Y) versus years (X). Let us suppose that the equation is the following: Y = 0.0015 * Exp (0.0063 * X).Give 5 examples of derivative of exponential function with solution