Name: Print Close During a lab experiment, bacteria are growing continuously at an exponential rate. The initial number of bacteria was 120, which increased to 420 after 5 days. If the bacteria continue to grow at the same rate, how many bacteria will there be after 8 days? 2,506 bacteria 600 bacteria 891 bacteria 57 bacteria Matt places $1,200 in an investment account earning an annual rate of 6.5%, compounded continuously. Using the formula V = Pe rt, where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, that Matt will have in the account after 10 years. Answer: $ 5. Solve the equation for x. Solve the equation for x. 27 Simplify: 6. A used car was purchased in July 2000 for $11,900. If the car depreciates 13% of its value each year, what is the value of the car, to the nearest hundred dollars, in July 2003? Answer: $ Page 1 of 10
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7. Solve the following equation for x. 9. Solve for x: 2 x + 1 = 4 x 2 6 3 12 9 8. Answer: Simplify the expression below. Reduce to lowest terms. 10. Which number is equal to 6 10 5? 360,000 0.000036 3,600,000 0.0000036 Page 3 of 10
1 Solve the equation 8 4x + 2y = 64 x + 2y for y in terms of x. 1 y = x y = x y = 2x The equation y = 24000 (0.93) t represents the depreciation of a new car purchased in 200 Which of the following explanations describes how the car s value changes year after year? 1 The value of the car depreciates by $1,680 each year. The value of the car increases by 93% each year. The value of the car decreases by 93% each year. The value of the car decreases by 7% each year. The equation: A = P(1 r) t can be used to model the decreasing population of bacteria, where t is the time in hours. The initial population was 100,000. After 5 hours, the population was 62,92 Find the rate of decrease as a percent. Round to the nearest hundredth of a percent. Answer: r = % 1 15. using radicals. On January 1, 1999, the price of gasoline was $39 per gallon. If the price of gasoline increased by 0.5% per month, what was the cost of one gallon of gasoline, to the nearest cent, on January 1 one year later? Answer: $ 16. Simplify the expression the result is in terms of positive exponents, only. x 2 y 3 so that Page 4 of 10
17. Since January 1980, the population of the city of Brownville has grown according to the mathematical model y = 720,500(022) x, where x is the number of years since January 1980. Which statement about this mathematical model is true? 720,500 represents the population in 1980, while the 022 represents a growth rate of 22% added to the current population. 720,500 represents the population in 1980, while 022 represents a growth rate of.22% added to the current population. 720,500 represents the population in 1980, while 022 represents a growth rate of 2% added to the current population. 720,500 represents the population in 1980, while 022 represents a growth rate of.022% added to the current population. 18. Solve the equation for x. 19. Simplify the expression in terms of positive exponents, only. 20. xy and leave the answer using radicals. Answer: x = 2 Dwayne purchased a computer from Techtronics, Inc. for $2,600 in 2007. The rate of depreciation is 7%. Which would be the best estimate for the value of the computer in 2010? $1,945 $2,577 $2,091 $2,593 Page 5 of 10
2 2 If f(x) = (x -x x 0 + 2 x ), then f(3) is equal to Rewrite the radical expression using exponents. 2 8 7-21 -22 Do not leave the answer in terms of a fraction. Use negative exponents when needed. Express in simplest form: 25. Answer: The solution set of {1} { 1,1} { 1} { } is 26. using radicals. x Page 6 of 10
27. The distance from Earth to the imaginary planet Med is 7 10 7 miles. If a spaceship is capable of traveling 1,420 miles per hour, how many days will it take the spaceship to reach the planet Med? Round your answer to the nearest day. 30. Simplify the expression positive exponents, only. so that it uses Answer: 28. days simplify. using radicals and 3 6 29. The population of Bridgeville, PA, is 5,300 with a growth rate of 3% per year. Which expression could be used to estimate the population of Bridgeville t years from now? 3(5300) t 5300(3) t 5300(013) t 5300t 3 The population of Henderson City was 3,381,000 in 2003, and is growing at an annual rate of 8%. If this growth rate continues, what will the approximate population of Henderson City be in the year 2009? 3,696,000 3,798,000 3,763,000 3,831,000 3 Which is a solution for the following equation? x = 16 x = 64 x = 32 x = 128 Page 7 of 10
3 using radicals. 3 The parents of twin boys started a college fund when the boys were 5 years old. They decided to invest $6,000 into an account that compounds quarterly at a rate of 8.6% annually. If the parents do not invest any additional money into this fund, how much will each of the boys have toward his education when they reach 18 years old? Use the formula:, where A is the amount at the end of a specific length of time, P is the initial amount of the investment, r is the rate as a decimal and t is time. Round your answer to the nearest cent. Answer: $ Page 8 of 10