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 Section: Chapter Questions
Problem 1RE: Determine whether the function y=156(0.825)t represents exponential growth exponential decay,... Problem 2RE: The population of a herd of deer is represented bythe function A(t)=205(1.13)t , where tis given... Problem 3RE: Find an exponential equation that passes through the points (2,2.25) and (5,60.75). Problem 4RE: Determine whether Table 1 could represent a function that is linear, exponential, or neither. If it... Problem 5RE: A retirement account is opened with an initialdeposit of 8,500 and earns 8.12 interest compounded... Problem 6RE: Hsu-Mei wants to save 5,000 for a down paymenton a car. To the nearest dollar, how much will sheneed... Problem 7RE: Does the equation y=2.294e0.654t representcontinuous growth, continuous decay, or neither?Explain. Problem 8RE: Suppose an investment account is opened with aninitial deposit of 10,500 earning 6.25... Problem 9RE: Graph the function f(x)=3.5(2)x. State the domainand range and give the y-intercept. Problem 10RE: Graph the function f(x)=4(18)x and its reflectionabout the y-axis on the same axes,... Problem 11RE: The graph of f(x)=6.5x is reflected about the y-axis and stretched vertically by a factor of 7. What... Problem 12RE: The graph below shows transformations of the graph of f(x)=2x. What is the equation for the... Problem 13RE: Rewrite log17(4913)=x as an equivalent exponentialequation. Problem 14RE: Rewrite ln(s)=t as an equivalent exponentialequation. Problem 15RE: Rewrite a25=b as an equivalent logarithmicequation. Problem 16RE: Rewrite e3.5=h as an equivalent logarithmicequation. Problem 17RE: Solve for xlog64(x)=(13) to exponential form. Problem 18RE: Evaluate log5(1125) without using a calculator. Problem 19RE: Evaluate log(0.000001) without using a calculator. Problem 20RE: Evaluate log(4.005) using a calculator. Round to thenearest thousandth. Problem 21RE: Evaluate ln(e0.8648) without using a calculator. Problem 22RE: Evaluate ln(183) using a calculator. Round to thenearest thousandth. Problem 23RE: Graph the function g(x)=log(7x+21)4. Problem 24RE: Graph the function h(x)=2ln(93x)+1. Problem 25RE: State the domain, vertical asymptote, and endbehavior of the function g(x)=ln(4x+20)17. Problem 26RE: Rewrite ln(7r11st) in expanded form. Problem 27RE: Rewrite log8(x)+log8(5)+log8(y)+log8(13) incompact form. Problem 28RE: Rewrite logm(6783) in expanded form. Problem 29RE: Rewrite ln(z)ln(x)ln(y) in compact form. Problem 30RE: Rewrite ln(1x5) as. a product. Problem 31RE: Rewrite logy(112) as a single logarithm. Problem 32RE: Use properties of logarithm to expand log(r2s11t14). Problem 33RE: Use properties of logarithms to expand ln(2bb+1b1) Problem 34RE: Condense the expression 5ln(b)+ln(c)+ln(4a)2 to a single logarithm. Problem 35RE: Condense the expression 3log7v+6log7wlog7u3 to a single logarithm. Problem 36RE: Rewrite log3(12.75) to base e. Problem 37RE: Rewrite 512x17=125 as a logarithm.Then applythe change ofbase formula to solve for x using thecommon... Problem 38RE: Solve 2163x216x=363x+2 by rewriting each sidewith a common base. Problem 39RE: Solve 125(1625)x3=53 by rewriting each side with a common base. Problem 40RE: Use logarithms to find the exact solution for 7179x7=49. If there is no solution, write nosolution. Problem 41RE: Use logarithms to find the exact solution for 3e6n2+1=60. If there is no solution, write nosolution. Problem 42RE: Find the exact solution for 5e3x4=6. If there isno solution, write no solution. Problem 43RE: Find the exact solution for 2e5x29=56. Ifthere is no solution, write no solution. Problem 44RE: Find the exact solution for 52x3=7x+1. Ifthere isno solution, write no solution. Problem 45RE: Find the exact solution for e2xex110=0. Ifthere is no solution, write no solution. Problem 46RE: Use the definition of a logarithm to solve. 5log7(10n)=5. Problem 47RE: Use the definition of a logarithm to find the exactsolution for 9+6ln(a+3)=33. Problem 48RE: Use the one-to-one property of logarithms to find an exact solution for log8(7)+log8(4x)=log(5). If... Problem 49RE: Use the one-to-one property oflogarithms to findan exact solution for ln(5)+ln(5x25)=ln(56). Ifthere... Problem 50RE: The formula for measuring sound intensity indecibels D is defined by the equation D=10log (II0),... Problem 51RE: The population of a city is modeled by the equation P(t)=256,114e0.25t where t is measured in years.... Problem 52RE: Find the inverse function f1 for the exponential function f(x)=2ex+15. Problem 53RE: Find the inverse function f1 for the logarithmicfunction f(x)=0.25log2(x3+1). Problem 54RE: For the following exercises, use this scenario: A doctor prescribes 300 milligrams of a therapeutic... Problem 55RE: For the following exercises, use this scenario: A doctor prescribes 300 milligrams of a therapeutic... Problem 56RE: For the following exercises, use this scenario: A soup with an internal temperature of 350... Problem 57RE: For the following exercises, use this scenario: A soup with an internal temperature of 350... Problem 58RE: For the following exercises, use this scenario: The equation N(t)=12001+199e0.625t models the number... Problem 59RE: For the following exercises, use this scenario: The equation N(t)=12001+199e0.625t models the number... Problem 60RE: For the following exercises, use this scenario: The equation N(t)=12001+199e0.625t models the number... Problem 61RE: For the following exercises, enter the data from each table into a graphing calculator and graph the... Problem 62RE: For the following exercises, enter the data from each table into a graphing calculator and graph the... Problem 63RE: For the following exercises, enter the data from each table into a graphing calculator and graph the... Problem 64RE: What is the carrying capacity for a population modeled by the logistic equation... Problem 65RE: The population of a culture of bacteria is modeled by the logistic equation P(t)=14,2501+29e0.62t... Problem 66RE: For the following exercises, use a graphing utility to create a scatter diagram of the data given in... Problem 67RE: For the following exercises, use a graphing utility to create a scatter diagram of the data given in... Problem 68RE: For the following exercises, use a graphing utility to create a scatter diagram of the data given in... Problem 1PT: The population of a pad of bottlenose dolphins ismodeled by the function A(t)=8(1.17)t, where... Problem 2PT: Find an exponential equation that passes throughthe points (0,4) and (2,9). Problem 3PT: Drew wants to save 2,500 to go to the nextWorld Cup. To the nearest dollar, how much willhe need to... Problem 4PT: An investment account was opened with aninitial deposit of 9,600 and earns 7.4 interest,compounded... Problem 5PT: Graph the function f(x)=5(0.5)x and its reflectionacross the y-axis on the same axes, and give... Problem 6PT: The graph below shows transformations of thegraph of f(x)=(12)x. What is the equation for... Problem 7PT: Rewrite log8.5(614.125)=a as an equivalentexponential equation. Problem 8PT: Rewrite e12=m as an equivalent logarithmicequation. Problem 9PT: Solve for x by converting the logarithmic equation log17(x)=2 to exponential form. Problem 10PT: Evaluate log(10,000,000) without using a calculator. Problem 11PT: Evaluate ln(0.716) using a calculator. Round to thenearest thousandth. Problem 12PT: Graph the function g(x)=log(126x)+3. Problem 13PT: State the domain, vertical asymptote, and endbehavior of the function f(x)=log5(3913x)+7. Problem 14PT: Rewrite log(17a2b) as a sum. Problem 15PT: Rewrite logt(96)logt(8) in compact form. Problem 16PT: Rewrite log8(a16) as a product. Problem 17PT: Use properties of logarithm to expand ln(y3z2x43). Problem 18PT: Condense the expression 4ln(c)+ln(d)+ln(a)3+ln(b+3)3 to a singlelogarithm Problem 19PT: Rewrite 163x5=1000 as a logarithm. Then applythe change of base formula to solve for x using... Problem 20PT: Solve (181)x1243=(19)3x1 rewriting eachside with a common base. Problem 21PT: Use logarithm to find the exact solution for 9e10a85=41. If there is no solution, writeno solution. Problem 22PT: Find the exact solution for 10e4x+2+5=56. If thereis no solution, write no solution. Problem 23PT: Find the exact solution for 5e4x14=64. Ifthere is no solution, write no solution. Problem 24PT: Find the exact solution for 2x3=62x1. If there isno solution, write no solution. Problem 25PT: Find the exact solution for e2xex72=0. If thereis no solution, write no solution. Problem 26PT: Use the definition ofa logarithm to find the exactsolution for 4log(2n)7=11. Problem 27PT: Use the one-to-one property of logarithms to find anexact solution for log(4x210)+log(3)=log(51) If... Problem 28PT: The formula for measuring sound intensityin decibels D is defined by the equation D=10log(II0) where... Problem 29PT: A radiation safety officer is working with 112 grams of a radioactive substance. After 17 days,... Problem 30PT: Write the formula found in the previous exerciseas an equivalent equation with base e. Express... Problem 31PT: A bottle of soda with a temperature of 71 Fahrenheit was taken off a shelf and placed ina... Problem 32PT: The population of a wildlife habitat is modeledby the equation P(t)=3601+6.2e0.35t where t isgiven... Problem 33PT: Enter the data from Table 2 into a graphing calculator and graph the ranking scatter plot. Determine... Problem 34PT: The population of a lake of fish is modeled by the logistic equation P(t)=16,1201+25e0.75t, where t... Problem 35PT:
Problem 36PT:
Problem 37PT:
Problem 33PT: Enter the data from Table 2 into a graphing calculator and graph the ranking scatter plot. Determine...
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PART 2
The pdf of the time to failure of an electronic component in a copier (in hours) is f (x ) = [exp (-x /3100)]/3100 for x > 0 and f (x ) = 0 for x ≤ 0. Determine the probability that:(d) Determine the number of hours at which 11% of all components have failed.(e) Determine the mean .
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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