Use a graphing utility to graph f and g in the same viewing window. Approximate the point of intersection of the graphs of f andg. Then solve the equation of f(x)g(x) algebraically. (Round your answer to three decimal places.)f(x) = 6 log5(x)%Dg(x) = 4Approximate point of intersectionSolution to f(x) = g(x)

Therefore from graph the point of intersection is (2.924 , 4)

Answered: Use a graphing utility to graph f and g…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.6: Exponential And Logarithmic Equations

Problem 79SE: Recall the formula for continually compoundinginterest, y=Aekt. Use the definition of a...

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Recall the formula for continually compoundinginterest, y=Aekt. Use the definition of a logarithmalong with Properties of logarithms to solve theformula for time t such that tis equal to a singlelogarithm.
The function f(x)=5x is an exponential function with base______; f(2) =_______, f(0) =______, f(2) =_______, and f(6) =_______.
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How the Logarithm IncreasesIf logx=8.3 and logy=10.3, how do x and y compare?
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More on the Pacific Sardine This is a continuation of Example 5.1. In this exercise, we explore the Pacific sardine population further, using the model in Example 5.1. a. If the current level of the Pacific sardine population is 50,000 tons, how long will it take for the population to recover to the optimum growth level of 1.2milliontons? Suggestion: One way to solve this is to make a new logistic formula using K2.4, r0.338, and N(0)0.05. b. The value of r used in Example 5.1 ignores the effects of fishing. If fishing mortality is taken into account, then r drops to 0.215 per year with the carrying capacity still at 2.4milliontons. Answer the question in part a using this lower value of r. Note: The population estimate of 50,000 tons and the adjusted value of r are given in the paper by Murphy see footnote 3 on page 347. Murphy points out that factoring in the growth of the competing anchovy population makes the recovery times even longer, and he adds. "It is disconcerting to realize how slowly the population will recover to its level of maximum productivity ... even if fishing stops." Studies to fit a logistic model to the Pacific sardine population have yielded. N=241+239e0.338t where t is measured in years and N is measured in millions of tons of fish. Part 1 What is r for the Pacific sardine? Part 2 According to the logistic model, in the absence of limiting factors, what would be the annual percentage growth rate for the Pacific sardine? Part 3 What is the environmental carrying capacity K? Part 4 What is the optimum yield level? Part 5 Make a graph of N versus t. Part 6 At what time t should the population he harvested? Part 7 What portion of the graph is concave up? What portion is concave down?
The natural logarithmic function f(x)= In (x1) has the ____________ asymptote x =____.

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