Quadratic equations Questions and Answers

The population of a county is growing at a rate of 9 per year compounded continuously How many years will it take for the population to quadruple according to the exponential growth function Round your answer up to the nearest whole number and do not include units

A population of bears increased by 50 in 4 years If the situation is modeled by an annual growth rate compounded continuously which formula could be used to find the annual rate according to the exponential growth function Leave your answer in terms of In Note When entering natural log in your answer enter lowercase LN as In There is no natural log button on the Alta keyboard Sorry that s incorrect Try again

In 2010 the population of the United States was approximately 310 million with a 0 97 annual growth rate At this rate the population P 1 in millions can be approximated by P t 310 1 0097 where I is the time in years since 2010 Part 1 of 5 a Is the graph of P an increasing or decreasing exponential function The graph of P is an increasing exponential function Part 1 5 Part 2 of 5 b Evaluate P 0 and interpret its meaning in the context of this problem P 0 This indicates that the U S population was approximately million in the year

The graph of a function is given Graph the inverse functic 7 6 5 th 6 5 T 3 19 3 2 1 2 3 4 5 6 7 1 2 3 4 5 6 H

How long will it take money to triple if it is invested at 9 compounded weekly 8 1 compounded continuously It will take about years at 9 compounded weekly Round to two decimal places as needed

Determine which of the given graphs is that of the function f x 5 x 3 x 1 x 1

10 0 4 x 7 1 7 Ok 2 2 6 4 2 10 10

A cylindrical water tank has a diameter of 41 ft and is 83 ft tall How many gallons of water can it store Write your answer in scientific notation with exactly four significant digits

Find the Cartesian equations for the curves r 4 sin 0 and 3 sec 0 Sketch the curves together and label their points of intersection in both Cartesian and polar coordinates

Sketch the line that you think best approximates the data in the scatter plot Then find an equation of the line To print an enlarged copy of the graph go to MathGraphs com y

Use Descartes Rule of Signs to determine the possible number of positive and negative real zeros Be sure to include all possibilities H x 2x4 19x 38x 133x 168 AnswerHow to enter your answer opens in new window Separate multiple answers with commas Araviened 2 Points Number of Positive Real Zeros 4 2 0 Keyp Keyboard Shor

Use the elementary properties of logarithms to solve the following equation Write your answer as a fraction reduced to lowest terms log 7x 5 Answertow

The revenue function is given by R x x p x dollars where x is the number of units sold and p x is the unit price If p x 37 5 find the revenue if 18 units are sold Round to two decimal places

848 The Metropolis Cab Company which has a fleet of 1000 taxis has divided the city into three zones with one office in each zone The matrix 0 42 0 33 0 12 shows the distribution of destinations from each zone For example 23 of the pickups in zone 1 are discharged in zone 3 After discharging a fare an MCC taxi waits in that zone for a new fare On the basis of this long term data what do you expect that the current distribution of MCC taxis is 0 35 0 48 0 31 0 23 0 19 0 57

Questions 3 8 use information from this table for Town A and Town B for a given year Town A Born Female Town B Born Female 100 300 350 150 Deaths among White persons Deaths among Non White persons Total Population at the midpoint of the year 5 500 Town A Born Male 175 225 8 500 Calculate the total crude mortality rate for Town A per 100 000 people 14 500 Town B Born Male 500 600 16 500

Maximize Q xy2 where x and y are positive numbers such that x y2 5 Cont B x 1 y 2 C x 0 y 5 5 A x 2 y 2 5 2 10 0 D x

Computers encode information in sequences of ones and zeros called bits One can estimate how many bits are needed to encode a positive integer n with the formula b log n where b is the estimated number of bits About how many bits are needed to encode the number 80 270 305 Round your answer to the nearest intege

List the zeros of the polynomial function f x 2x x 2 in ascending order Then provide the multiplicity of each zero and determine if the graph crosses or touches the x axis at the x intercept First zero Second zero Multiplicity Multiplicity Touches or Crosses the axis answer t or c Touches or Crosses the axis answer t or c

8 pts Solve the system of equations You may use any method of your choice but your method must be algebraic not graphical If the system is inconsistent state there are no solutions If the system is dependent express the solution set in terms of one of the variables 2y z 3x 2y 2 x 2 x 2 4 z 4 1 y

Use the vertex h k and a point on the graph x y to find the general form of the equation of the quadratic function

Suppose the tangent line to the curve y f x at the point 2 1 has the equation y 5 2x If Newton s method is used to locate a solution of the equation f x 0 and the initial approximation is x 2 find the second approximation X2 X2

Consider two functions y1 f x y 1 f x and y2 g x y 2 g x and that y1 y2 y 1 y 2 except where they intersect If these two functions intersect at 253 places how many different integrals do you need to find the total area enclosed by the two curves

g w w 4 2w w 2x 7x 6 X 2 y 5x 2 4 f x 4 ln 2x 3x r2 2r3

2 Solve the logarithmic equation log5 x 2 log 5 x 2 log1 5 x 2 4 6 Marks Hint Use the change of base formula to break down every term into log with base 5

points 1 0 hoose 3 inequalities that form a system whose graph is the shaded region shown above Click on the graph to enla A 8x 5y2 17 B y 2 3 C 8x 4y 2 28 D x 3 E x 3 Fy 3

An installment contract for the purchase of a car requires payments of 200 87 at the end of each month for 4 25 years Interest is 4 per annum compounded monthly a What is the amount financed b How much is the interest cost a The amount financed is S Round the final answer to the nearest cent as needed Round all intermediate values to six decimal places as needed

Solve 92 5 6 Enter an exact answer or round your answer to the nearest tenth Do not include in your answer Provide your answer below

Find the required annual interest rate to the nearest tenth of a percent for 1100 to grow to 1700 if interest is compounded quarterly for 10 yr The required annual interest rate is Round to the nearest tenth as needed

How long to the nearest day will it take any quantity of a radioactive element to decay to 25 of its initial amount knowing that it decays according to the exponential function A t Age 0 081t where t is the time in days It will take days to decay to 25 of its initial amount Do not round until the final answer Then round to the nearest integer as needed

Find the coordinates of the point on the parametric curve described below for whent 3 3t 14 y 7 15t 38 13 41 13 13 38

Tabitha has a 25 000 student loan at an interest rate of 4 35 that is compounded monthly for 12 years Calculate Tabitha s monthly payment rounding to the nearest cent Provide your answer below

Jona is saving up money for a down payment on a townhouse He currently has 5959 but knows he can get a loan at a lower interest rate if he can put down 6533 If he invests the 5959 in an account that earns 5 5 annually compounded continuously how long will it take Jona to accumulate the 6533 Round your answer to two decimal places if necessary Keypad

A senior executive decides running is a good way to manage stress Initially only 0 4 miles could be run at a time Each 0 3w 0 4 where mis week an additional 0 3 miles was added to the run This can be modeled by the equation m total miles and wis number of weeks Use this model to predict the length of a run in week 5 Provide your answer below miles

A college student has an account with 3200 in it Each month 70 is withdrawn from that account to pay the cell phone bill That is the only activity on this account This can be modeled by the equation A 70m 3200 Use this equation to predict the amount of money in the account after 3 months Provide your answer below

The temperature at 4 00 AM was 6 degrees Fahrenheit Each hour the temperature increased 7 degrees What is the slope in this situation Do not include units in your answer Provide your answer below

QUESTION 1 1 POINT Carl placed 3 700 in a savings account that compounds interest annually at a rate of 2 0 How much will he have in the account after 10 years Round your answer to the nearest dollar Do NOT round until you have calculated the final answer Provide your answer below

Reduce each fraction to lowest terms if possible If it is already reduced to lowest terms choose already reduced to lowest terms x x 6 x 3 3x 5 3x 60 12 3000 45 x x 6 x 3 8 27 3x 2x 8 3x 4 1 already reduced to lowest terms 1 x 2 2 3 x 2 4 x2 5 1 x 2 6 5

2x 4x48 0 Select all of the correct solutions You may choose more than one answer 0x 4 x 4 0x 2 x 2 0x 8 O x 8 x 6 x 6

Multiply Simplify the following x 6 x 36 x O 6x 36 Ox 12x 36 2 X Ox 12x 12 2

Solve the following equation using the quadratic formula x 10x 22 0 Choose the best answer from below The answers have been slightly simplified after using the quadratic formula O X x 10 100 88 2 Ox X 22 484 40 2 x 10 100 88 2 10 100 88 2 None of these

Solve the following equation using the square root method 4x 1 0 2 Give your answer in simplified rationalized form Ox 1 Or 1 2 4 0x 1 1 201 O 11 x None of these

Solve the following equation using the square root method x 4 0 Give your answer in simplified rationalized form 0x 2 0x 2i x 4 None of these

If a sample of a certain solution is determined to have a a H3O concentration of 9 72 x 10 moles liter what is its pH Round off your answer to one decimal place Keypad

y 2 tan x n 3 Period Phase shift Asymptote 1 x Asymptote 2 x values and then click on at the basic graph POUR Enter Use 2 6

Use the change of base theorem to find the logarithm log 1 5 9 Use the change of base theorem to rewrite the given expression in terms of natura logarithms or common logarithms log 1 5 Do not evaluate Do not simplify 9

e2x 16ex 63 0 What is the solution in terms of natural logarithms Select the correct choice below a if necessary fill in the answer box to complete your choice O A The solution set is Use a comma to separate answers as needed Type an exact answer in simplified form OB The solution set is the empty set

The height H x in meters of an object after x seconds is approximated by the following equation A negative height means the object is below sea lev H x 8x 33x 33 4x 16x 17 Complete the following a Use the ALEKS graphing calculator to find the value of x that minimizes the height Then give the minimum height Round your answers to the nearest hundredth Value of x that minimizes height seconds Minimum height meters b Complete the following sentence For very large x the height appears to Choose one

The concentration of a drug in a patient s bloodstream after t hours is modeled by the formula C t 11 0 74 where C is measured in milligram per liter a What is the initial concentration of the drug b How long does it take for the concentration to decrease to 70 of its initial level a The initial concentration of the drug is milligrams per liter CLER

Given g x ex evaluate each of the following a g In 5 b g In 4 c a in 27 g In a g ln 5 Simplify your answer

Write an equation for the inverse function of the one to one function given f x log 21x Simplify your answer