College Algebra 1st Edition
ISBN: 9781938168383
Author: Jay Abramson
Publisher: Jay Abramson
1 Prerequisites 2 Equations And Inequalities 3 Functions 4 Linear Functions 5 Polynomial And Rational Functions 6 Exponential And Logarithmic Functions 7 Systems Of Equations And Inequalities 8 Analytic Geometry 9 Sequences, Probability And Counting Theory Chapter6: Exponential And Logarithmic Functions
6.1 Exponential Functions 6.2 Graphs Of Exponential Functions 6.3 Logarithmic Functions 6.4 Graphs Of Logarithmic Functions 6.5 Logarithmic Properties 6.6 Exponential And Logarithmic Equations 6.7 Exponential And Logarithmic Models 6.8 Fitting Exponential Models To Data Chapter Questions Section6.7: Exponential And Logarithmic Models
Problem 14TI: The half-life of plutonium-244 is 80,000,000 years. Find function gives the amount of carbon-14... Problem 15TI: Cesium-137 has a half-life of about 30 years. If we begin with 200 mg of cesium-137, will it take... Problem 16TI: Recent data suggests that, as of 2013, the rate of growth predicted by Moore’s Law no longer holds.... Problem 17TI: A pitcher of water at 40 degrees Fahrenheit is placed into a 70 degree room. One hour later, the... Problem 18TI: Using the model in Example 6, estimate the number of cases of flu on day 15. Problem 19TI: Does a linear, exponential, or logarithmic model best fit the data in Table 2? Find the model. Problem 20TI: Change the function y=3(0.5)x to one having e as the base. Problem 1SE: With what kind of exponential model would half-life be associated? What role does half-life play in... Problem 2SE: Is carbon dating? Why does it work? Give an example in which carbon dating would be useful. Problem 3SE: With what kind of exponential model would doubling time be associated? What role does doubling time... Problem 4SE: Define Newton’s Law of Cooling. Then name at least three real-world situations where Newton’s Law of... Problem 5SE: What is an order of magnitude? Why are orders of magnitude useful? Give an example to explain. Problem 6SE: The temperature of an object in degrees Fahrenheit after t minutes is represented by the equation... Problem 7SE: For the following exercises, use the logistic growth model f(x)=1501+8e2x . 7. Find and intercept... Problem 8SE: For the following exercises, use the logistic growth model f(x)=1501+8e2x . Find and interpret f(4).... Problem 9SE: For the following exercises, use the logistic growth model f(x)=1501+8e2x . Find the carrying... Problem 10SE: For the following exercises, use the logistic growth model f(x)=1501+8e2x . Graph the model. Problem 11SE: For the following exercises, use the logistic growth model f(x)=1501+8e2x . Determine whether the... Problem 12SE: For the following exercises, use the logistic growth model f(x)=1501+8e2x . Rewrite f(x)=1.68(0.65)x... Problem 13SE: For the following exercises, enter the data from each table into a graphing calculator and graph the... Problem 14SE: For the following exercises, enter the data from each table into a graphing calculator and graph the... Problem 15SE: For the following exercises, enter the data from each table into a graphing calculator and graph the... Problem 16SE: For the following exercises, enter the data from each table into a graphing calculator and graph the... Problem 17SE: For the following exercises, use a graphing calculator and this scenario: the population of a fish... Problem 18SE: For the following exercises, use a graphing calculator and this scenario: the population of a fish... Problem 19SE: For the following exercises, use a graphing calculator and this scenario: the population of a fish... Problem 20SE: For the following exercises, use a graphing calculator and this scenario: the population of a fish... Problem 21SE: For the following exercises, use a graphing calculator and this scenario: the population of a fish... Problem 22SE: For the following exercises, use a graphing calculator and this scenario: the population of a fish... Problem 23SE: A substance has a half-life of 2.045 minutes. If the initial amount of the substance was 132.8... Problem 24SE: The formula for an increasing population is given by p(t)=P0ert where P0 is the initial population... Problem 25SE: Recall the formula for calculating the magnitude of an earthquake, M=23log(SS0) . Show each step for... Problem 26SE: What is the y -intercept of the logistic growth model y=c1+aerx ? Show the steps for calculation.... Problem 27SE: Prove that bx=exln(b) for positive b1 . Problem 28SE: For the following exercises, use this scenario: A doctor prescribes 125 milligrams of a therapeutic... Problem 29SE: For the following exercises, use this scenario: A doctor prescribes 125 milligrams of a therapeutic... Problem 30SE: For the following exercises, use this scenario: A doctor prescribes 125 milligrams of a therapeutic... Problem 31SE: For the following exercises, use this scenario: A tumor is injected with 0.5 grams of Iodine-125,... Problem 32SE: For the following exercises, use this scenario: A tumor is injected with 0.5 grams of Iodine-125,... Problem 33SE: For the following exercises, use this scenario: A tumor is injected with 0.5 grams of Iodine-125,... Problem 34SE: For the following exercises, use this scenario: A tumor is injected with 0.5 grams of Iodine-125,... Problem 35SE: For the following exercises, use this scenario: A tumor is injected with 0.5 grams of Iodine-125,... Problem 36SE: For the following exercises, use this scenario: A tumor is injected with 0.5 grams of Iodine-125,... Problem 37SE: For the following exercises, use this scenario: A tumor is injected with 0.5 grams of Iodine-125,... Problem 38SE: For the following exercises, use this scenario: A biologist recorded a count of 360 bacteria present... Problem 39SE: For the following exercises, use this scenario: A biologist recorded a count of 360 bacteria present... Problem 40SE: For the following exercises, use this scenario: A pot of boiling soup with an internal temperature... Problem 41SE: For the following exercises, use this scenario: A pot of boiling soup with an internal temperature... Problem 42SE: For the following exercises, use this scenario: A pot of boiling soup with an internal temperature... Problem 43SE: For the following exercises, use this scenario: A turkey is taken out of the oven with an internal... Problem 44SE: For the following exercises, use this scenario: A turkey is taken out of the oven with an internal... Problem 45SE: For the following exercises, use this scenario: A turkey is taken out of the oven with an internal... Problem 46SE: For the following exercises, find the value of the number shown on each logarithmic scale. Round all... Problem 47SE: For the following exercises, find the value of the number shown on each logarithmic scale. Round all... Problem 48SE: For the following exercises, find the value of the number shown on each logarithmic scale. Round all... Problem 49SE: For the following exercises, find the value of the number shown on each logarithmic scale. Round all... Problem 50SE: For the following exercises, use this scenario: The equation N(t)=5001+49e0.7t models the number of... Problem 51SE: For the following exercises, use this scenario: The equation N(t)=5001+49e0.7t models the number of... Problem 52SE: For the following exercises, use this scenario: The equation N(t)=5001+49e0.7t models the number of... Problem 53SE: For the following exercise, choose the correct answer choice. A doctor and injects a patient with 13... Problem 14TI: The half-life of plutonium-244 is 80,000,000 years. Find function gives the amount of carbon-14...
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Concept explainers
Why might one prefer to use the logarithmic differentiation for finding derivatives of functions that have another function as an exponent?
The question basically means why we should use logarithmic differentiation when finding derivative of functions in the form of f(x)g(x) .
With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.
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