Sequences & Series Questions and Answers

The number of bacteria in a certain population is predicted to increase according to a continuous exponential growth model at a relative rate of 14 per hour Suppose that a sample culture has an initial population of 82 bacteria Find the population predicted after five hours according to the model Do not round any intermediate computations and round your answer to the nearest tenth bacteria

The mass of a radioactive substance follows a continuous exponential decay model with a decay rate parameter of 5 2 per day Find the half life of this substance that is the time it takes for one half the original amount in a given sample of this substance to decay Note This is a continuous exponential decay model Do not round any intermediate computations and round your answer to the nearest hundredth days X S

The amount of money invested in a certain account increases according to the following function where y is the initial amount of the investment and y is the amount present at timer in years 0 045 y yo After how many years will the initial investment be doubled Do not round any intermediate computations and round your answer to the nearest tenth years in D 14

15 cos x sin x 9 0 Separate multiple solutions with a comma If there are no solutions please enter no solution exactly Submit Question Question 16 Find the exact solutions to sin x cos x in the interval 0 27 If the equation has no solutions respond with DNE Submit Question Question 17 0 10 pts 598 Det Find all solutions on the interval 0 2m Give exact answers 3 33 10 pts 597 Detai

A certain loan program offers an interest rate of 3 5 compounded continuously Assuming no payments are made how much would be owed after four ye on a loan of 1900 Do not round any intermediate computations and round your answer to the nearest cent 1 X

Find the amount that results from the given investment 100 invested at 3 compounded quarterly after a period of 2 years After 2 years the investment results in S Round to the nearest cent as needed REEB

What is the vertex of the absolute value function f x x al b where a and b are real numbers Choose the correct answer below OA a b OB a b OC a b OD a b

Use the function value to find the indicatod trigonometric value in the specified quadrant Function Value Quadrant Trigonometric Value COM 1 cso 0

Graph the line that has an x intercept of 2 0 and y intercept of 0 2 5 4 3 2 7 5 V 3 2 1 7 2 3 4 5 2 3 S

Is y 37x 26 increasing or decreasing decreasing increasing

You Try QUESTIONS 1 2 Determine whether the following function Graphical and by looking at the Equatio Verify algebraically a f x x 1 1 52 0 b f x

1 Find the slope of the line passing through the given points a 4 1 2 5 b 2 3 6 5 c 3 2 3 6 d 1 7 4 1 2 Find the x and y intercepts for each of the following equations of lines a 2x 3y 18 b 5x 4y 20 c y x 4 d y x 2 3 Find the slope and the y intercept for each of the following lines a 6x5y 10 b 3x 4y 12 c 2x 3y 6 d 4x y 3 4 Graph each of the above lines in problem 3 using slope and the y intercept

on 7 area of a triangle bound icular to f x that passe

oring 2023 ements ons Question 8 Year 1950 2000 The median home value in Virginia Virginia 39900 125400 Oregon 41500 152100 that the house valu

Brightpoint COMMUNITY COLLEGE Account Dashboard 071 Courses Groups Brightpoint Spring 2023 Home Announcements Syllabus Modules Discussions Grades Zoom 16 Brainfuse Tutoring Question 1 In 2003 a school population was 1 How much did the population g st 2 How long did it take the popul y 3 What is the average populatio

Hightpoint Community College Chester Midlothian ng 2023 ments S 16 Tutoring Due Sunday by 11 59pm Points HW Section 2 3 Score 0 8 0 8 answered Question 2 The phone company Splint has a and then a certain amount of mo minutes the monthly cost will be 307 A Find an equation in the form y y is the total monthly cost of the

16 bring Question 4 Suppose that the world reserves is decreasing A Give a linear equati the number of years si R B 10 years from now CUE no other oil is del

6 5 4 3 2 1 4 3 2 0 2 3 0 0 1 2 Return this question to its initial state On the graph make the two lines parallel The dashed line is given by the equation 3x 4y 16 What is the slope of the dashed line 3 What is the slope of any line parallel to the dashed line

Find the distance and midpoint if the following points below Enter your answer in as a whole number or fraction You are expected to simplify whenever possible If your answer contains a radical then use sqrt For Example 2 sqrt 2 or 2 2 2sqrt 2 P 5 7 and Q 13 1 D MP

Let f x 2x 3 and let g x x 3 find and simply the following whenever possible Enter in your answer as a whole number or fraction gog 2 I

Choose the answer that best describes the graph Percent of radioactivity 100 80 60 40 20 of 0 O increasing O decreasing O constant O neither both Decay of Carbon 14 Radioactivity vs time 60000 Time years 20000 40000 80000 80000 100000

The population of a small town is decreasing at a rate of 4 each year The following table shows a projection of the population N after t years 0 1 2 3 4 O Year O 14 5 years 15 5 years 13 9 years 7 900 If the population of the small town is currently 7 900 people how many years will it take for the population to reach 4 300 people 14 9 years 7 584 7 281 6 989 6 710 Population

To train for an upcoming marathon Susie plans to run 2 miles per day the first week and then increase the daily distance by half a mile each of the following weeks How long before the marathon should she start There are many ways to approach this problem Some include making a table writing a function creating ordered pairs 1 Identify and label the variables 2 Make a table for up to 6 weeks to see a pattern 3 Write an equation to represent the nth term of the sequence 4 If the pattern continues during which week will she run 10 miles per day 5 Is it reasonable to think that this pattern will continue indefinitely Explain 6 How long before the marathon should she start

plane flies 450 miles with the wind and 350 miles against the wind in the same mount of time If the wind is blowing at 30 mph how fast would the plane be going thout air helping hurting 453 4 15 115

y 3 7 6 5 4 2 3 x 7 6 1 D 5 2 O 2 3 10 5 6 3 5 O 9

2 n 5 4 3 2 1 5 y 5 4 3 2 b II 1 H 5 4 3 2 1 2 3 4 st Find a formula for each of the transformations whose graphs are given below Recall that square root is entered as sqrt a 3 24 5 2 3 4 St 5 4 3 2 1 i 32 3 2 3 8 2 5 1 2 3 2 3 4 5 1 2 3 a

If the formula y 2 is changed by adding four as shown in red below Which of the following best describes the resulting change for each of the functions Function f x x 4 f x x 4 Transformation a The 4 would directly affect the y values so the graph would shift vertically b The 4 would have no effect c The 4 would directly affect the x values so the graph would shift horizonally

Find a logarithmic equation that relates y and x Round all numerical values to three decimal pla 2 3 5 in 6

The function h x defined as f x 1 x 1 can be expressed in the form f g x where g x x 1 and f x is

Now complete the summary of all the reduction formulas found in previous sections by referring to question 1 4 2 4 3 4 4 4 5 6 4 and 7 4 above QUADRANT 2 sin 180 8 cos 180 8 tan 180 8 sin 90 6 cos 90 8 QUADRANT 3 sin 180 0 cos 180 8 tan 180 8 sin 8 cos B tan 8 QUADRANTI sin 360 8 cos 360 8 tan 360 8 sin 90 8 cos 90 8 sin 0 cos 0 tan 8 QUADRANT 4 sin 360 9 cos 360 8 tan 360 8 2

14 What is the perimeter of this figure 4x3 x 3x A B 2x 1 Perimeter A a B x C 000 x 1

3 5 pts Consider the following series 3 3 3 ln x ln x 4 16 Find for which x it converges and for which x the total sum is equa

a Expand and simplify 1 3 b By writing 75 as 30 45 find the value of cos 75 The following diagram shows the triangle ABC where BC 6 CA 2 and ACB 75 A 6 c Find AB in the form a b where a b e Z B 2 75

Write an equation for the function graphed below 7 6 5 4 y 3 2 1 I 5 4 13 I 2 1 1 2 3 4 5 2 3 5 6 7 Q

The equation y 2 3 shows the number of infected people from an outbreak of the norovirus The variable y represents the number of infected people and t represents time in weeks In how many weeks will the number of infected people reach 1 458 O a 5 weeks O O b 12 weeks c 6 weeks d 10 weeks

Determine the number of ways in which 2023 can be written as a1 a2 a3 an where n 2 is a positive integer a1 a2 a3 an are positive integers and al an 1

Solve Round to the nearest 4 19 on Answer Check Solve Round to the nearest ten thousandth 23x4 5 Answer Check Solve by graphing on a calculator Round to nearest ten thousandth 53x 500 Answer Check

The Venn diagram here shows the cardinality of each set Us A n A 13 C 6 12 9 6 B

Suppose that A and B are sets such that ACB Which of the following must be true Select all that apply O A AUB A B AUB B C AnB A OD AnB B E A B 0 OF B A 0 OG ACB OH RCA

Which of the sets given below correspond to the following Venn Diagram Select all that apply A C A C An B B C AUB C C A n C B D C A U C B E ANB nC OF AUB nc G ANB UC H AUB UC B U

t a local college 88 of the male students are smokers and 712 are non smokers Of the female students 162 are smokers and 648 are non smokers A male tudent and a female student from the college are randomly selected for a survey What is the probability that both are smokers Do not round your answer

Available Medication A liquid 25mg mL How many ounces would you administer Round to the nearest tenth

a Provide a rational function satisfying all of the conditions Has a vertical asymptote at x 2 and x 3 Has a horizontal asymptote at y 1 Has x intercepts at 3 and 4 b For the following polynomial please give the x intercept s the vertical asymptote s the y intercept and the horizontal asymptote f x x 6x 8 x 4x 3

The graph of y f x is shown Draw the graph of y f x b The graph of y g x is shown Draw the graph of y g x

Dosage Ordered Cycanocobalamin 0 3 mg How many mL s should the nurse administer Round to the nearest tenth

Order Heparin 2500 units Available Heparin 10 000 units mL How many mL s would you administer Round to the nearest hundredth

In order to accumulate enough money for a down payment on a house a couple deposits 374 per month into an account paying 3 compounded monthly If payments are made a the end of each period how much money will be in the account in 5 years Type the amount in the account

In Problems I through 4 you given four sequenes of please do 2 things First describe in your own words any observations about the sequences Specifically what similarities do they have What differences do they have What patterns do you notice Second please calculate the 10th term for each sequence 1 22 10 4 1 In the space below f4 12 2 3 12 48 192 768

Simplify each expression Answer with positive exponents only a 5a b 5a c 5a 1 Submit Question

The milligrams of aspirin in a person s body is given by the equation a 500 1 How much aspirin will be in the patient s body after two hours 2 In the equation what does the 500 tell us about the situation 3 3 In the equation what does the tell us about the situation 4 4 Graph the equation for values of t between 0 and 4 below the text box 34 t where t is the number of hours since the patient took the medicine