UNIT #6 EXPONENTS, EXPONENTS, AND MORE EXPONENTS REVIEW QUESTIONS

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1 Name: Date: UNIT #6 EXPONENTS, EXPONENTS, AND MORE EXPONENTS REVIEW QUESTIONS Part I Questions 1. The epression can be simplified to (1) 6 () () (4). Which of the following is equivalent to (1) 6 () 8? () 1 6 (4) 1 8. If f 10 then which of the following represents the value of 0 (1) 1 () 10 () 0 (4) 0 f? 4. Which of the following is the equation of an increasing eponential function? y () y5 (1) () y 7 (4) y 4 5. If Jordan had his hourly salary increase from $9.5 per hour to $10.75 per hour, which of the following is closest to the percent increase in Jordan's salary? (1) 8% () 16% () 14% (4) 19%

2 6. Which of the following could be the equation of the eponential function shown below? (1) y 0.9 () y y () y (4) y The population of Ketcham High School has been decreasing by 5% per year. If its population is currently,600 students, which of the following is closest to its population two years from now? (1),40 (),470 (),47 (4), A population of bacteria is increasing at a rate of 7.5% per hour. If there were originally 75 bacteria, which of the following equations models the population of bactera h-hours after the original 75 bacteria were measured? (1) h P () P 1.075h 75 () P h (4) P h 9. If the first two terms of a geometric sequence are 4 and 1, which of the following would be the 10 th term? (1) 76 () 78,7 () 84 (4) 6, A radioactive material has a mass given by mt t, where the mass is in grams and the time, t, is in years. Which of the following gives the average rate of change of the mass over the interval t 5 years? (1) 1.1 grams per year () 6. grams per year () 18. grams per year (4) 8.9 grams per year

3 Free Response Questions 11. Simplify the following epression. Write it in two ways, one with the use of negative eponents and one with the use of a fraction (that doesn't have negative eponents) Simplify the following epression An object's speed can be modeled with the equation S t, where S represents its speed in miles per hour and t represents the amount of time that has passed, in seconds. Give an interpretation of the parameters 4 and 1.06 from the equation. 14. An eponential function, f, is shown in the table below. Determine an equation for it in f ab form. 0 1 f

4 15. Ma deposits money into a savings account that earns.5% interest applied annually. If Ma initially deposits $450 into the account, how much money does the account hold after 5-years if Ma does not deposit or withdraw any additional money? Show how you arrived at your answer. 16. Determine the equation of the eponential function shown graphed below. Eplain how you arrived at your answer. 17. A function passes through the points 0, 8 and 1, 4. (a) Write the equation of a linear function that passes through these two points and write the equation of an eponential function that passes through these two points. Linear, y m b Eponential, y a b (b) How much greater is the eponential function's value at 5 than the linear function's value? Show how you arrived at your answer.

5 18. A geometric sequence is defined using the following rule: f 0 4 and f n f n 1 Find the fourth term of the sequence. Show how you arrived at your answer. 19. Which is larger, the 10th term of an arithmetic sequence that begins with the terms 0 and 100 or the 10th term of a geometric sequence that begins with the terms 5 and 10? Show work that justifies your answer. 0. A local newspaper claims that the number of flu cases is increasing eponentially. On Monday, there were 8 flu cases reported. On Tuesday, there were 1 flu cases and on Wednesday there were 4 cases reported. On Thursday, there were 0 flu cases. Was the newspaper's claim of eponential increase accurate? Justify your response. 1. The first three terms of a geometric sequence are shown below. Write a recursive rule for this sequence. 16, 144, 96 What is the net term of the sequence?