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Answered: 1 Use the change of base formula to…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.6: Exponential And Logarithmic Equations

Problem 74E

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Use log21=0,log22=1, and log24=2 to estimate log23.
Recent data suggests that, as of 2013, the rate of growth predicted by Moore’s Law no longer holds. Growth has slowed to a doubling time of approximately three years. Find the new function that takes that longer doubling time into account.
Suppose an investment account is opened with aninitial deposit of 10,500 earning 6.25 interest,compounded continuously. How much will theaccount be warm after 25 years?
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.
Since the data obtained as a result of 5 observations of an experiment is ∑ log Xi = 6.27, what is the geometric mean of this experiment?
A start-up firm has kept careful records of the time required to manufacture itsproduct, a shutoff valve used in gasoline pipelines.Cumulative Number Number of Hours Requiredof Units Produced for Next Unit50 3.3100 2.2400 1.0600 0.81,000 0.510,000 0.2a. Compute the logarithms of the numbers in each column. (Use natural logs.)b. Graph the ln(hours) against the ln(cumulative units) and eyeball a straight-linefit of the data. Using your approximate fit, estimate a and b.c. Using the results of part (b), estimate the time required to produce the first unitand the appropriate percentage learning curve that fits these data.d. Repeat parts (b) and (c), but use an exact least squares fit of the logarithmscomputed in part (a).
4. The population of Lalaland is 600,000 currently and is expected to grow (continuously) at 3.5% per year. Determine what the population will be in 4 decades (i.e. 40 years)?
A CERTAIN RADIOACTIVE MATERIAL IS KNOWN TO DECAY AT A RATE PROPORTIONAL TO THE AMOUNT PRESENT. IF AFTER ONE HOUR IT IS OBSERVED THAT 10% OF THE MATERIAL HA DECAYED, FIND (a) AN EXPRESSION OF THE MATERIAL REMAINING AT ANY TIME (b) FIND THE HALF-LIFE MATERIAL.
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? deer
A quantity with an initial value of 840 decays continuisly at a rate of 5% per day. What is the value of the quantity after 10 weeks, to the nearest hundredth?
Since the data obtained as a result of 10 observations of an experiment is ∑ log niXi = 8.2431, what is the geometric mean of this experiment?

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1 Use the change of base formula to compute logo 5 Round your answer to the nearest thousandth.