The function is defined for all values of x. Therefore, the domain is set of all real numbers.
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1 Graph each function. State the domain and range. 1. f (x) = 3 x The function is defined for all values of x. Therefore, the domain is set of all real numbers. The value of f (x) tends to 2 as x tends to. The value of f (x) tends to as x tends to. Therefore, the range of the function is {f (x) f (x) > 2}. 2. The function is defined for all values of x. Therefore, the domain is set of all real numbers. The value of f (x) tends to as x tends to. The value of f (x) tends to 3 as x tends to. Therefore, the range of the function is {f (x) f (x) > 3}. esolutions Manual - Powered by Cognero Page 1
2 Solve each equation or inequality. Round to four decimal places if necessary c + 1 = 16 2c esolutions Manual - Powered by Cognero Page 2
3 5. 2 a + 3 = 3 2a 1 6. log 2 (x 2 7) = log 2 6x By Zero Product Property: The x-value 1 makes the argument negative. Logarithm is not defined for negative numbers. Therefore, the solution is log 5 x > 2 esolutions Manual - Powered by Cognero Page 3
4 8. log 3 x + log 3 (x 3) = log 3 4 By Zero Product Property: The x-value 1 makes the argument negative. Logarithm is not defined for negative numbers. Therefore, the solution is n 1 11 n esolutions Manual - Powered by Cognero Page 4
5 10. 4e 2x 1 = ln (x + 2) 2 > 2 Use log and log to approximate the value of each expression. 12. log 5 44 esolutions Manual - Powered by Cognero Page 5
6 POPULATION The population of a city 10 years ago was 150,000. Since then, the population has increased at a steady rate each year. The population is currently 185,000. a. Write an exponential function that could be used to model the population after x years if the population changes at the same rate. b. What will the population be in 25 years? a. Substitute , 10 and for y, t and a in the equation y = a(1 + r) t then solve for r. The annual rate of growth for this city is about The exponential function that models the population after x years from the current date is y = 185,000(1.0212) x. b. Substitute 185,000 for a, for r, and 25 for x in y = a(1 + r) t then evaluate for y The population will be about 312,56 in 25 years. esolutions Manual - Powered by Cognero Page 6
7 15. Write in exponential form. 16. AGRICULTURE An equation that models the decline in the number of U.S. farms is y = 3,962,520(0.98) x, where x is the number of years since 1960 and y is the number of farms. a. How can you tell that the number is declining? b. By what annual rate is the number declining? c. Predict when the number of farms will be less than 1 million. a. Since the base of the exponential is less than one (b < 1), the number is declining. b. The number is declining by 0.02 or 2%. c. Substitute 1,000,000 for y and solve for x. Therefore, the number of farms will be less than 1 million in about 2028( ). esolutions Manual - Powered by Cognero Page 7
8 17. MULTIPLE CHOICE What is the value of A 3 B C D 3 Option A is the correct answer. esolutions Manual - Powered by Cognero Page 8
9 18. SAVINGS You put $7500 in a savings account paying 3% interest compounded continuously. a. Assuming there are no deposits or withdrawals from the account, what is the balance after 5 years? b. How long will it take your savings to double? c. In how many years will you have $10,000 in your account? a. Substitute 7500, 0.03 and 5 for P, r and t respectively in the continuous compound interest formula then evaluate. b. Substitute 15000, 7500 and 0.03 for A, P and r then solve for t. The principal will take approximately 23.1 years to double. c. Substitute 10000, 7500 and 0.03 for A, P and r then solve for t. You will have $10,000 in your account about 9.6 years. esolutions Manual - Powered by Cognero Page 9
10 19. MULTIPLE CHOICE What is the solution of log 4 16 log 4 x = log 4 8? F G 2 H 4 J 8 Option G is the correct answer. 20. MULTIPLE CHOICE Which function is graphed below? A y = log 10 (x 5) B y = 5 log 10 x C y = log 10 (x + 5) D y = 5 log 10 x Function of the given graph is y = log 10 (x + 5) Option C is the correct answer. esolutions Manual - Powered by Cognero Page 10
11 21. Write as a single logarithm. esolutions Manual - Powered by Cognero Page 11
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