<p>ALGEBRA U6 HW 6-1 Linear vs Exponential Functions</p><p>1 1. Use the function f(x) = x  5 to fill in the table below and graph. 2</p><p> x f(x)</p><p>0 a) What type of function is this 1 and why?</p><p>2</p><p>3 b) What is the rate of change? 4</p><p>5 c) 6 What is the domain?</p><p> d) What is the range?</p><p> x  1  2. Use the function g(x) =   to fill in the table below and graph.  3</p><p> x g(x)</p><p>-3 a) What type of function is this and why? -2</p><p>-1 b) What is the 0 rate of change?</p><p>1</p><p>2 c) What is the domain? 3</p><p> d) What is the range?</p><p>3. Two band mates have only 7 days to spread the word about their next performance. Walt thinks they can each (Walt AND Allie) pass out 100 fliers a day for 7 days and they will have done a good job in getting the news out. Allie has a different strategy. She tells 10 of her friends about the performance on the first day and asks each of her 10 friends to each tell a friend on the second day and then everyone who has heard about the concert to tell a friend on the third day and so on, for 7 days (assume that students make sure they are telling someone who has not already been told). </p><p> a) Fill in the tables below: </p><p>Walt Allie</p><p>(day) (people x reached) f(x)</p><p>1 10</p><p>2 100</p><p> b) What type of function is illustrated by Walt’s table? Explain.</p><p> c) What type of function is illustrated by Allie’s table? Explain.</p><p> d) Which band mate’s idea would reach more people, Walt’s or Allie’s? 4. Which of the following represents an expression?</p><p>(1) x  7  4 (3) 3x 2  5</p><p>(2) 5x  8  12 (4) 2X  2  30</p><p>ALGEBRA U6 HW 6-2 Identifying Functions</p><p>Identify the following equations as Linear, Quadratic, or Exponential. Justify your choice.</p><p>1. 2x2  3  18 ______2. 3  5x  20 ______</p><p>3. 2a  3ax 2  24 ______4. 5x  125 ______</p><p>5. 30  6x  8 ______6. 64  4x ______</p><p>7. Do the examples below require a linear or exponential growth model? </p><p> a. An alligator population starts with 200 alligators and every year, the alligator population is 9/7 of the previous year’s population. </p><p> b. The temperature increases by 2° every 30 minutes from 8:00 a.m. to 3:30 p.m. for a July day that has a temperature of 66° at 8:00 a.m.</p><p> c. Arnold does 5 sit-ups on Monday. Each day increases his set by 1 more than the previous day. By Saturday he can do 10 sit-ups.</p><p> d. In a bank account for Antwain’s college fund there is $5,000. Each year the account increases by 1.5%. 8. Which situation could be modeled by using a linear function?</p><p>(1) A bank account balance that grows at a rate of 5% per year, compounded annually (2) A population of bacteria that doubles every 4.5 hrs (3) The cost of cell phone service that charges a base amount plus 20 cents per minute (4) The concentration of medicine in a person’s body that decays by a factor of one-third very hour</p><p>9. The table below shows the balance in a savings account for different years. </p><p>Does it illustrate a linear or exponential function? Justify your answer.</p><p>Year Balance, in Dollars</p><p>0 380.00</p><p>10 562.49</p><p>20 832.63</p><p>30 1232.49</p><p>40 1824.39</p><p>50 2700.54</p><p>10. The function represents the height, ,in feet, of an object from the ground at seconds after it is dropped. A realistic domain for this function is</p><p>(1) (2) (3) (4) all real numbers</p><p>11. Which of the following points is a solution to the system of inequalities? </p><p>(1) (1,1) (3) (4, 2)</p><p>(2) (2, -2) (4) (-2, -1)</p><p>12. The perimeter of a triangle can be represented by the expression 5x2 – 10x + 8. Write a polynomial that represents the measure of the third side. x2 - x - 4</p><p>3x2 - 4x + 5</p><p>ALGEBRA U6 HW 6-3 Exponential Growth & Decay</p><p>For questions #1-4:</p><p> a. State whether it is a growth or decay. b. State the initial value. c. State the rate of growth or decay.</p><p>1. c(t) = 100(.75)t 2. p(n) = 40(1.80)n</p><p>3. t(x) = 10,000(1.02)x 4. f(n) = 50(.1)n</p><p>5. A huge ping-pong tournament is held in Beijing, with 65,536 participants at the start of the tournament. Each round of the tournament eliminates half the participants. </p><p> a. If 𝑝(𝑟) represents the number of participants remaining after 𝑟 rounds of play, write a </p><p> formula to model the number of participants remaining. </p><p> b. Use your model to determine how many participants remain after 10 rounds of play. c. How many rounds of play will it take to determine the champion ping-pong player? </p><p>6. A construction company purchased some equipment costing $300,000. The value of the equipment depreciates at a rate of 14% per year. </p><p> a. Write a formula C(t) that models the value of the equipment. </p><p> b. What is the value of the equipment (to the nearest dollar) after: i) 2 years?</p><p> ii) 4 years?</p><p> iii) 6 years?</p><p> iv) 8 years?</p><p> v) 10 years? </p><p> c. Graph the points from part b on the grid below (including t = 0). </p><p> t C(t)</p><p>0 2 4 6 8 10 What type of function does the graph show?</p><p>______</p><p>ALGEBRA U6 HW 6-4 Exponential Growth & Decay</p><p>1. The value of an early American coin increases in value at the rate of 6.5% annually. If the purchase price of the coin this year is $1,950, what is the value to the nearest dollar in 15 years?</p><p>2. In 1985, there were 285 cell phone subscribers in the small town of Centerville. The number of subscribers increased by 75% per year after 1985. How many cell phone subscribers were in Centerville in 1994? </p><p>3. Solve the following system algebraically. </p><p>2x + 5y = 2 y = 3x – 20 4. Solve for x: </p><p>5 2 x  4  x  7 9 9</p><p>11. Given f (n)  2x3  2 x , find f (5)</p><p>ALGEBRA U6 HW 6-5 Simple & Compound Interest</p><p>1. $250 is invested at a bank that pays 7% simple interest. Calculate the amount of money in the account after 1 year; 3 years; 7 years; 20 years?</p><p>2. $325 is borrowed from a bank that charges 4% interest compounded annually. How much is owed after 1 year; 3 years; 7 years; 20 years?</p><p>3. A youth group has a yard sale to raise money for a charity. The group earns $800 but decided to put its money in the bank for a while. Calculate the amount of money the group will have if: </p><p> a. Cool Bank pays simple interest at a rate of 4% and the youth group leaves the money in for 3 years. </p><p> b. Hot Bank pays compound interest at a rate of 3% and the youth group leaves the money in for 3 years (same). </p><p> c. If the youth group needs the money quickly (in about 3 years), which is the better choice? Why?</p><p>4. Joseph has $10,000 to invest. He can go to Yankee Bank that pays 5% simple interest or Met Bank that pays 4% interest compounded annually. </p><p># of years Yankee Bank (add P) Met Bank</p><p> a. Fill in the table above for the 14 years. </p><p> b. Write a formula for the interest he will earn after 𝒕 years at Yankee Bank. </p><p> c. Write a formula for the total amount he will have after 𝒕 years at Met Bank. 5. Carly is babysitting at $8 per hour to earn money for a car. So far she has saved $1300. The car that Carly wants to buy costs at least $5440. How many full hours must Keisha still work in order to have enough money to buy the car?</p><p>REVIEW QUESTIONS:</p><p>6. State the rate of change (Positive or Negative) shown in each table below. </p><p>______</p><p>7. In a piggy bank on his dresser, Tom has a total of $2.85 in pennies and quarters. If the number of Tom’s pennies is 5 more than three times the number of quarters, how many pennies and quarters does he have in the piggy bank?</p><p>8. Which equation below represents an exponential function? (1) 4x 2  3  19 (3) 3x  7  25</p><p>(2) 5x  125 (4) 12  2x  5</p><p>9. If x – 1 represents an odd integer, what represents the next greater odd integer?</p><p>(1) x (2) x + 2 (3) x – 3 (4) x + 1 </p><p>10. Which equation represents a line that is parallel to the line whose equation is 2x – 3y = 9?</p><p>2 (3) 3 y  x  4 y  x  4 (1) 3 2</p><p>(2) 2 (4) 3 y   x  4 y   x  4 (2) 3 2</p>