Logarithms Questions and Answers

Which statement best describes market capitalism Market capitalism is one in which the government does not have the power to alter price by taxation and cannot interfere with the quantity demanded by consumers Market capitalism is one in which the government determines the methods of production by creating laws that restrict production of certain goods Market capitalism is one in which the government has the power to add taxes to price altering the quantity demanded by consumers Market capitalism is one in which the government operates in a laissez faire mode and does not influence the factors of production Complete Later Complete

ef D d Credit card A is running a promotion whe then 0 8 compounded continuously afte compounded continuously If you are go single payment for 2 5 years which credi the total balance at the end of 2 5 years t

Archaeologists used pieces of burned wood or charcoal found at the site to date prehistoric paintings and drawings on walls and ceilings of a cave in Lascaux France Use the information in Exampl of Section 3 1 to determine the appropriate age of a piece of burned wood if it was found that 82 5 of the C 14 found in living trees of the same type had decayed Round your answer to the nearest hundred years ANOTHE years

A large tank is filled to capacity with 600 gallons of pure water Brine containing 4 pounds of salt per gallon is pumped into the tank at a rate of 6 gal min The well mixed solution is pumped out at the same rate Find the number A t of pounds of salt in the tank at time t A t lb

The table below shows some input output pairs for an exponential function f 1 3 7 129 1667 34 7121 9 3285 X f x a What is the 1 unit growth factor b What is the initial value of f f 0 2023 11 2 5069

In the circular flow diagram a labor flows from households to firms O b goods flow from households to firms c services flow from households to firms O d profit flows from households to firms

A competitive market is a market in which a an auctioneer helps set prices and arrange sales b the forces of supply and demand do not apply c no individual buyer or seller has any significant impact on the market price O d there are only a few sellers

List the roots of the parabola y x 18x 106 In other words list the solutions of the equation 0 x 18x 106 x Your answers must be in exact form do not give their decimal values Separate multiple roots with a comma

A new sofa cost 1200 in 2010 The value of the couch decreases by 15 per year a Write a formula for the value of the couch t years after 2010 b If the cost continues to decrease exponentially what will the value of the sofa be in 5 years c If the cost continues to decrease exponentially how long will it take for the couch to reach half of its original price

A market failure occurs when O a retailer cannot fill consumer demand with product on hand O economic decisions are made with a lack of information O a wholesaler cannot fill retail orders due to lack of inventory products are pulled from the market before it reaches the decline phase

1 In a certain culture of bacteria the rate of increase is proportional to the number present a If it is found that the number doubles in 4 hours how many may be expected at the end of 12 hours b If there are 104 at the end of 3 hours and 4 x 10 at the end of 5 hours how many were there at the beginning

Country A has an exponential growth rate of 4 8 per year The population is currently 5 779 000 and the land area of Country A is 10 000 000 000 square yards Assuming thill growth rate continues and is exponential after how long will there be one person for every square yard of land

3 Find the value of n 2 100 In n 1 n Hint In the proof of FTOC I we en countered a telescoping sum Are these telescoping possibly in disguise i e after equivalently re writing the general term

Paul sells office equipment He earns 2 000 each month plus 18 commission In August he sold 21 000 worth of equipment Find the total amount of his paycheck

Uriel used a 245 00 payday loan to pay a bill The finance charge on the loan was 21 00 with a 16 00 transaction fee If the term was 14 days what was the APR of Uriel s loan Round the final answer to nearest hundredth 4 points O 340 56 405 56 393 73 425 46

Are you ready for more A bank account is growing exp was 1 200 At the beginning of balance be at the beginning of expression Fran 2 slic

The actual delivery time from a pizza delivery company is exponentially distributed with a mean of 26 minutes a What is the probability that the delivery time will exceed 31 minutes b What proportion of deliveries will be completed within 21 minutes 0 a The probability that the delivery time will exceed 31 minutes is Round to four decimal places as needed GW

Element X decays radioactively with a half life of 5 minutes If there are 890 grams of Element X how long to the nearest tenth of a minute would it take the element to decay to 48 grams t

Write the Hindu Arabic numeral as a Mayan numeral 4827 Choose the correct answer below O A 0 02 10 L N 2 3 www 111 13 OB 4 14 5 15 16 7 17 8 18 9 19 OC

If y 2x 5 2x 5x then dy dx Be sure to express your answer in terms of x

Using infinite series and special values find the value of the following integral C In 1 x X dx m N Find a closed form using Riemann Zeta function

A temporary diversion has been constructed on a highway of 4 percent grade due to major repairs that are being undertaken on a bridge The maximum speed allowed on the diversion is 20 mi h Determine the minimum distance from the diversion that a road sign should be ocated informing drivers of the temporary change on the highway Assume that a driver can read a road sign within his or her area of vision at a distance of 30 ft for each inch of letter height speed limit on highway 65 mi h letter height of road sign 8 in perception reaction time 2 5 sec

Let f x Using the definition of derivative f x f a f a x a a enter the expression needed to find the derivative at x 2 f 2 4x 12x 3 lim lim x 2 X Don t use f notation here use the actual given function for your response Also don t simplify too much After evaluating this limit we see that f 2 Finally the equation of the tangent line to f x where x 2

The ambient temperature Tm in 3 in Section 1 3 dT dt dT xT Tm or K T Tm 3 dt could be a function of time t Suppose that in an artificially controlled environment Tm t is periodic with a 24 hour period as illustrated in the figure below Tm 140 120 100 80 60 40 20 70 20 cos nt 12 t 12 24 36 48 Noon Midnight Noon Midnight Devise a mathematical model for the temperature T t of a body within this environment Use T for T t

A cup of coffee cools according to Newton s law of cooling 3 in Section 1 3 dT dt 3 dT dt Use data from the graph of the temperature T t in the figure to estimate the constants Tm Tor and k in a model of the form of a first order initial value problem dT dt k T Tm T 0 To Tm To x T T m TA 200 150 100 50 I 0 or K T Tm 25 50 75 100 t minutes

Graph the line with y intercept 5 and slope 4

3 Consider the following list of properties i ii iii iv v lim f x x 1 lim f x x 1 lim f x 2 x 1 f 1 3 lim f x x1 For each of the following decide if it is possible for a function to have the given set of properties If so sketch and label a possible graph for the function on the axis provided If no such function is possible explain why not a i and ii b i iii and iv c i iii and v d iv and v

Write The of a expression as the logarith single number or expression Assume that all variables represent positive numbers 3 In x 18 In x 7 simplify your ansuer

7 8 7 35 log x 1 0 2 1 1 624 107 x 1 8 46 3 42 log Find value of X I know answer comes out to be 9 2 But when i try to solve it using calculator such big equation does not fit I need how to break down this so i can use calculator to completely solve it 900 0 75 690 0 75 1 122 1 166

Find the value of the expression log 5 53 O A 15 OB 5 O C 125 D 3

Use a calculator to find the common logarithm log 13 The answer is

X 60 40 20 0 20 40 60 0 20 40 60 80 100 0 Degrees 120 140 160 18

log log M r Fr log M Substitution log 3 Properties of exponents Logarithm property log b c Substitution Commutative property of multiplication Which expression is missing from the proof log log 6

Rewrite the following logarithms in expanded form by applying the properties of logarithm 2 0 a log b log 8y

ewrite the logarithmic equation in exponential form JE log 127

17 Evaluate the logarithm without using a calculator 1 a log 2 b log c log 164 d log 842

16 Solve for x and round the answer to the nearest tenth a 3 38 b 2 19 c 4 7

An ecosystem with mature trees has a relatively constant population of beetles species 1 around 106 At t 0 a single reproducing invasive beetle species 2 is introduced accidentally If species 2 grows at the exponential rate N t 0 39t at what rate is species 2 growing when the population of species 2 exceeds species 1 O a 3900000 0000 O b 65000 0000 O c 157 3372 O d 390000 0000 O e 39000 0000 O f 1000000 0000

Calculate Social Security taxes Medicare taxes and FIT for Jordon Barrett He earns a monthly salary of 12 900 He is single Before this payroll Barrett s cumulative earnings were 142 045 Social Security maximum is 6 2 on 142 800 and Medicare is 1 45 Calculate FIT by the percentage method Use Table 9 1 Note Round your answers to 2 decimal places FIT Social Security taxes

Find the area of the shaded region 4 Points x 6 x 94 x

The numbers of students in the 10 schools in a district are given below Note that these are already ordered from least to greatest 171 207 230 270 276 285 305 328 378 440 Send data to calculator Suppose that the number 440 from this list changes to 220 Answer the following a What happens to the median b What happens to the mean O It decreases by O It increases by 0 O It stays the same O It decreases by O It increases by 0 O It stays the same

Consider the following table and assume that fox and g x are differentiable functions with values as given 1 2 3 4 X 26 54 0 1 1 g 3 3 0 7 6 6 33 ro 95 2179 86 x 87 4 1 2 5 4 7 x Calculate h 3 if a 33 70 O b 13 70 Oc 10 00 d This derivative does not exist e 5 40 1270 A z 1 z 49 2

Rewrite the expression without the log of a product power or root 1083 2 5

24 The perimeter of a rectangle is 40 inches and the area of the rectangle is 96 square inches Use system of equations to find the dimensions of the rectangle

9 a 4 points Solve for x and round the answer to the nearest tenth 5 11 b 4 points Evaluate the logarithm without using a calculator log 32

Suppose you have the function y= -log(x). a) What is the base of the log? b) Complete the table using the given function, y= -log(x). Round to the nearest unit. x y 1 10 100 1000 c) What is happening to the y values in the table in part b? d) Are the x-values in the table in part b increasing by 10 or by a factor of 10? e) Use part c and d to write a statement to describe the meaning of the base in the function y = -log(x).

Solve the equations below. Check for extraneous solutions. Please show all work for full credit. log2x- log8= 3 What logarithmic property did you use in order to solve? log(x+1)+ log(x - 1) = log 8 What logarithmic property did you use in order to solve?

Solve the equation. logx4=2 Change the given logarithmic equation to exponential form. (Type an equation. Do not simplify.) The solution set is __). (Type integers or simplified fractions. Use a comma to separate answers as needed.)

Write the following expression as a sum and/or difference of logarithms. Express powers as factors. In [e (x+8)] In [e (x + 8)] = (Simplify your answer.)

This problem has two parts. Part 1: Suppose log (p) = 6 and log(q) = − 7. 1. The value of log (p³ q²) is____________ 2. The value of log((p^(-2)*q^3)^(1/4)) is__________ 3. One way to express in terms of p and q is k^4=________ 4. If log (r) = 26, one way to express r in terms of p and q is r =______