Logarithms Questions and Answers

dath 1111 Te wh Question 19 1 point Analyze the graph of the function R x 1 What is the domain of R x A x x 0 8 x x 5 5 C x x 0 25 D x x 5 E All real numbers For part 1 the answer is Type a letter 2 What is the equation of vertical asymptote s of R x A x 0 B x 5 5 C x 0 25 D x 5 E There is no vertical asymptote x x 10 x 25x A 3 What is the equation of the horizonta or oblique asymptote of R x A y 0 B y 1 C y 10 D y x E There is no horizontal or oblique asymptote

Construct a polynomial function F zeros 1 1 and 4 degree 3 y intercept 12 Choose the correct answer below Of x 2 x 1 x 1 x 4 Of x 3 x 1 x 1 x 4 f x 3 x 1 x 1 x 4 2 2 x 1 x 1 x 4

Differentiate y 11 7

Lee is saving up money for a down payment on a condominium He currently has 2651 but knows he can get a loan at a lower interest rate if he can put down 3236 If he invests the 2651 in an account that earns 3 9 annually compounded quarterly how long will it take Lee to accumulate the 3236 Round your answer to two decimal places if necessary Answer How to enter your answer opens in new window Keypad Keyboard Shortcuts

Use the following to answer questions 18 19 Figure Demand and Supply of Gasoline Price per gallon 5 4 3 2 50 2 1 50 1 0 S2 D 100 200 300 400 500 600 Quantity of gasoline per month Figure Demand and Supply of Gasoline Look at the figure Demand and Supply of Gasoline A factor that may have changed supply from S to S is A better technology in the production of gasoline B increased demand C lower labor productivity in gasoline production D increased prices of substitutes for gasoline Figure Demand and Supply of Gasoline Look at the figure Demand and Supply of Gasoline Given the initial equilibrium of S and D any price lower than W create pressure for the price to A 2 00 fall B 2 50 rise C 3 00 rise

Computational exercise Write a script to use Runge Kutta method of order 4 to compute an approx imate solution to y y t y t for 1 t 2 y 1 1 h 0 1 Please attach your script and give your final approximation to y t 2 The exact solution is y t t 1 In t

3 Determine the change in enthalpy Ah for oxygen O in kJ kg as it is heated from 300 K to 1000 K using constant specific heat evaluated at 300 K a 712 kJ kg b 643 kJ kg c 461 kJ kg d 275 kJ kg e 918 kJ kg

Use the Consumer Price Index below to answer the question Average Annual Consumer Price Index 1982 1984 100 Year CPI Year CPI 1986 109 6 188 9 1987 113 6 195 3 1988 118 3 201 6 1989 124 0 207 3 1990 130 7 215 3 1991 136 2 214 5 1992 140 3 218 1 1993 144 5 224 9 1994 148 2 229 6 Year CPI 152 4 156 9 160 5 163 0 166 6 172 2 177 1 179 9 184 0 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 22 Suppose you needed 43 000 to maintain a particular standard of living in 1986 How much would you have needed in 1994 to maintain the same standard of living A 32 000 B 58 000 C 54 000 D 61 000 23 Suppose you needed 56 000 to maintain a particular standard of living in 2000 How much would you have needed in 1990 to maintain the same standard of living A 44 000 B 41 000 C 43 000 D 74 000 22 23

1 point Let Find A and use it to solve where where x1 and 2 A 3 3 5 AX B B X Note In order to get credit for this problem all answers must be correct 3 24 X2

Consider the future value of the following 627 at 5 5 compounded quarterly for 4 years Give the future value for compound interest formula where A is the future value in dollars P is the present value in dollars r is the annual interest rate as a decimal n is the number of compounding periods each year and t is the time in years A Determine the following values P T n t Find the future value using the future value formula and a calculator Round your answer to the nearest cent

Solve for x log42 log4 x 3 log49 X 0 3 N solu

Solve for x 102x 10 10 24 0 Round to the nearest hundredth if necessary If there is more than one solution separate them with commas x 0 0 0

Write the expression as a single logarithm 4 log log logx 2log y log w

Rewrite each equation as requested a Rewrite as an exponential equation lnx 5 b Rewrite as a logarithmic equation e 9 a b 0 Olog In 3 0 0

oblem 2 An isotope of sodium has a half life of 15 hours A sample of this isotope has an initial mass of 2 g a Write an exponential function that models the amount remaining after t hours b Estimate the amount remaining after 4 hours c Estimate the time required for the mass to be reduced to 0 01 g

29 A 90 m basement in a residence is found to be contaminated with radon coming from the ground through the floor drains The concentration of radon in the room is 1 5 Bq L under steady state conditions The room behaves as a CSTR and the decay of radon is a first order reaction with a decay rate con stant of 2 09 106 s If the source of radon is closed off and the room is vented with radon free air at a rate of 0 14 m s how long will it take to lower the radon concentration to an acceptable level of 0 15 Bq L

A person bought a car for 21 022 After 3 years the car was worth 11 984 Assume that the price is decreasing according to the continuous exponential decay model P Poet a Find the annual depreciation rate r to the nearest tenth of a percent b Find the value of the car after 5 years to the nearest hundred dollars a What is the annual depreciation rate Do not round until the final answer Then round to one decimal place as needed

After the end of an advertising campaign the daily sales of a product fell rapidly with daily sales given by S 3900e 0 12x dollars where x is the number of days from the end of the campaign a What were daily sales when the campaign ended b How many days passed after the campaign ended before daily sales were below half of what they were at the end of the campaign a The daily sales when the campaign ended were Simplify your answer Round to the nearest cent as needed ACCES

004131 The formula A 21 26 models the population of a US state A in millions t years after 2000 Determine algebraically when the population was predicted to reach 29 8 million The population of the state will reach 29 8 million in the year Round up to the nearest year SCITE

6 5x2 8 6 6 2 4x

Consider a function of x equal to the determinant shown below f x 0 2 2 3 The first derivative f x of this function with respect to x is equal to O O 4x 6x5 3x 3x 8x4 5 x6 O 3x4 1 6

There are typically 31 gallons of beer in a standard barrel What is Shannon s market share in gallons if it brews and sells 3 430 barrels in 2014 Express your answer in percent to two decimal places Assume the total market size in barrels sold is 194 472 Do not include the symbol For example if you compute a market share of 5 785 percent you should enter 5 79

Draw a number line with a bell curve drawn above it Show work calculating and placing the usual seven numbers under the number line mean 3 to the left and 3 to the right if the mean equals 55 6 and the standard deviation equals 7 5 If all the space area under your bell curve to the number line represents 100 50 on each side of the mean what would you estimate the percentage of shaded space area from the number 70 6 and to the left Use the Empirical Rule as your guide pg 110 and or Ch 3 PowerPoint slide 35 Show your detailed calculations and shaded bell curve Answer Do not draw a new number line or make a new shading but if you were asked to hypothetically shade under the bell curve from the number 48 1 and to the left what would you estimate that shaded area to be out of 100 Show your detailed calculations

A country has a national debt of 8 x 10 2 If the population of the country is 400 million people how much will it be for every man woman and child in the country Every person will owe Type an integer or a decimal

3 Identify the vertical and horizontal asymptotes of the function 2 x 3x 4 f x 20 ylenavni z9nDy fiuprio loohibele no ni zov 290 3 x Sai eppotaizen en nertw stlov Of al tubo ant ne

1 Show that f using the expressions for and f in Cartesian coordinates Use result from a the product rule for divergence fF f F f F an df the chain rule for gradient Vf g g to show that dg f r f f r 2f r dr r for a function f of r the magnitude of 7 Hint Let g r and recall from class that Vr f

For the evidence below the author provides In a 2017 press release Spotify reported that it had approximately 100 million active users in 60 countries Strong Source Information and a Strong Reporting Verb Weak Source Information

19 Which of the following is the best description of an oxidation process OA Oxidation is the gain of electrons OB Oxidation is the loss of electrons OC Oxidation is the non spontaneous loss of electrons OD Oxidation is the spontaneous loss of electrons

Perform steps 1 4 of the algorithm once The value of p is fill in blank value of x after step 3 is fill in blank SUBMIT and the Problem Convert the decimal number 42 to a binary number in engineering notation with the exponent in c Determine the bit sequence for the mantissa if 10 bits are available for the mantissa Algorithm 1 Let x be the number to translate find p the largest power of 2 smaller equal to x log a log 2 P PEZ n p 2 How many times does 2 fit into the number 1 if 2 x 0 otherwise 3 Set x to the remainder of the number not yet translated

or the 3 x 3 matrix A the singular value decomposition is A USV where U u 02 03 Use MATLAB to compute the dot product di dor u1 U so use MATLAB to compute the cross product c cross u and dot product d dot c u3 Clearly state the values for each of these computations Do these values make sense Explain olution

Date 8 11 23 Find the rational fraction in lowest terms represented by the periodic decimal 1 0 44444

In a chemical process the amount of a certain type of impurity in the output is difficult to control is thus a random variable Speculation is that the population mean amount of the impurity is 0 20 grams per gram of output It is known that the standard deviation is 0 1 grams per gram of output An experiment is conducted to gain more insight regarding the speculation that the population mean is 0 20 a The process was run on a lab scale 50 times and the sample average x turned out to be 0 23 grams per gram Perform analysis and comment on the speculation on the population mean b What if the process was run 30 times and the sample average x turns out to be 0 19 grams per gram

Which of the following is the first stage of joining clusters in agglomerative hierarchical clustering O by joining two clusters that are closest to each other O by joining two clusters farthest away from each other O by separating clusters into finer groups O by joining two clusters that are not at a Euclidean distance

21 You check the patient s IV and find that there is 200 mL of fluid remaining in the bag If you are to hang a new bag by the time there are 50 ml remaining how soon should you return The drop factor is 15 and the drop rate is 25 gtt min

Select the appropriate equation that matches the graph 01 y 1 5 02y x 5 O3 y x 5

As a tornado moves its speed increases The function S d 90 log d 70 relates the speed of the wind S in miles per hour near the center of a tornado to the distance that the tornado has travelled d in miles Determine the distance that a tornado has travelled if the speed of the wind at the center of the tornado reaches 150 miles per hour

If 8 g of a radioactive substance are present initially and 5 yr later only 4 0 g remain how much of the substance to the nearest tenth of a gram will be present after 11 yr After 11 yr there will be g of the radioactive substance Do not round until the final answer Then round to the nearest tenth as needed

Solve the equation x d 2y dx 2 2 dy dx 2 dy dx

8 TI When you drink a cup of coffee or a glass of cola or when you eat a chocolate bar the percent P of caffeine remaining in your bloodstream is related to the elapsed time t in hours by the following equation t logP log 0 5 5 a How long will it take for the amount of caffeine to drop to 20 of the amount consumed b Supposed you drink a cup of coffee at 9 00 am what percent of the caffeine will remain in your body at noon

a b The voltage V in a circuit is given by V 3R 135R 1800R 200 where R is the resistance in ko 1 Compute dV dR Compute R values of turning point Compute whether R makes a maximum voltage or minimum voltage If y x show that logarithmic differentiation dy dx 2x 1 x 3 marks 3 marks 4 marks 1 by 6x In x 3 at the point x x 3 10 marks

How do you find the function values for f x log5 if your calculator does not allow you to directly evaluate logarithms with a base of 5 Write an equivale expression for log5 x

Use properties of logarithms to evaluate the expression without using a calculator 4 log25 5 8 log25 5 log25 625

Use the properties of logarithms to expand each logarithm as much as possible When possible select from the dropdown instead of entering a negative number a log y 7 log x log y b ln y Y ln y In 4 y 4 y

State a function that accurately represents the wave function that is shown in the graph Use sine State exact values 10 15 9 10 15 Edit View Insert Format Tools Table 20 35

3 2 points Which of the following is equivalent to the expression 2 4 a 9x y 16 b 144x y C 9x 81 8 X 8 144

Imagine you are building a decision tree to predict whether a personal loan given to a person would result in a payoff i e the person pays off the loan or default the person fails to pay back the loan Your entire data set consists of 30 examples 16 belong to the default class 14 belong to the payoff class The examples contain two features Balance and Residence Balance refers to the amount of money the person has in their savings and checking accounts at the time of the loan which can take on two values 50K or a 50K o Residence refers to whether or not the person owns their home or rents and can take on two values OWN or RENT As stated the class label for y can be either default or payoff Before splitting the parent region into child regions the entropy of y in the parent region is H y parent 30 log 30 log 3 0 99 After splitting the parent region into two child regions CL and CR the weighted average of the entropy of y over the child regions is the sum r CL H y CL r CR H Y CR where r CL is the ratio of the number of examples in child region c divided by the number of total examples in the parent region prior to a split r CR is the ratio of the number of examples in child region CR divided by the number of total examples in the parent region prior to a split The goal is to find a good split that will yield a low weighted average entropy of the partitioned child regions Calculate the entropy for the parent node and see how much uncertainty exists by splitting on Balance The blue circles represent people from the payoff class and the red circles are people from the default class Splitting the parent node on the Balance attribute gives us two child nodes 50K or 50K Review the graphic below to see how the data is split 0 37 Entire population 30 instances 0 99 Balance 50K p 12 13 0 92 p 1 13 0 08 12 1 16 0 14 p 16 30 0 53 p 14 30 0 47 p 4 17 0 24 p 13 17 0 76 What is the entropy of the root node if we split on Balance Balance 50K 4 13

a What is the equation of the profit function P x for this commodity Recall that to find the total profit P x we subtract the total cost C x from the total revenue R x Select the equation for the profit function P x R x C x P x C x R x P x R x C x P x C x R x P x R x x C x Step 2 Now substitute the functions R x 371x and C x 71x 3 300 into P x R x C x Simplify the result by collecting like terms P x R x C x P x 371x 71x 3300

A person who believes that they are primarily responsible for the outcomes in their life has an O External locus of control Internal validation model Internal locus of control External validation model K

1 point Which of the following graphs are trees 1 A graph G with V G a b c d e and E G a b a c b c c d d e 2 A graph G with V G a b c d e and E G a b a c a d a e Care 3 A graph G with V G a b c d e and E G a b a e b c c d d e 4 A graph G with V G a b c d e and E G a b b c c d d e Note In order to get credit for this problem all answers must be correct

Write this decimal in numbers thirty three and forty seven hundredths