practice exercises 9_MAT-1210-GS-sep22

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MAT-1210: COLLEGE ALGEBRA Kristi Stevenson Practice Exercises 9 SECTION 6.1 Algebraic For the following exercise, identify whether the statement represents an exponential function. Explain. 1. The height of a projectile at time is represented by the function h ( t )=− 4.9 t 2 + 18 t + 40 . This is not an exponential function it is a polynomial function. It does not follow the exponential formula of f(x) = ab x For the following exercise, consider this scenario: For each year the population of a forest of trees is represented by the function A ( t )= 115 ( 1.025 ) t . In a neighboring forest, the population of the same type of tree is represented by the function B ( t )= 82 ( 1.029 ) t . (Round answers to the nearest whole number.) 2. Which forest had a greater number of trees initially? By how many? A ( t )= 115 ( 1.025 ) t A(t) has a greater number of trees by 34. For the following exercise, determine whether the equation represents exponential growth, exponential decay, or neither. Explain. 3. y = 16.5 ( 1.025 ) 1 x The equation is neither growth nor decay since the exponent in the form of 1 x is not an exponential equation. For the following exercise, find the formula for an exponential function that passes through the two points given. 4. ( 3,1 ) ( 5,4 ) This work, “Practice Exercises 9,” is a derivative of College Algebra 2e by Jay Abramson, OpenStax used under CC BY 4.0 . “Practice Exercises 9” is licensed under CC BY 4.0 by Thomas Edison State University.
For the following exercise, use the compound interest formula, A ( t )= P ( 1 + r n ) nt . 5. After a certain number of years, the value of an investment account is represented by the equation A ( t )= 10,250 ( 1 + r 0.4 12 ) 120 What is the value of the account? After 10 years the value of the account is $524,296.02 Numeric For the following exercise, evaluate each function. Round answers to four decimal places, if necessary. 6. f ( x )= 2.7 ( 4 ) x + 1 + 1.5 , for f (− 2 ) Technology For the following exercise, use a graphing calculator to find the equation of an exponential function given the points on the curve. 7. ( 3,222.62 ) ( 10,77.456 ) . f ( x )= 350.000032 ( 0.8600004889 ) x Real-World Applications 8. A scientist begins with 100 milligrams of a radioactive substance that decays exponentially. After 35 hours, 50 mg of the substance remains. How many milligrams will remain after 54 hours? This work, “Practice Exercises 9,” is a derivative of College Algebra 2e by Jay Abramson, OpenStax used under CC BY 4.0 . “Practice Exercises 9” is licensed under CC BY 4.0 by Thomas Edison State University.
This work, “Practice Exercises 9,” is a derivative of College Algebra 2e by Jay Abramson, OpenStax used under CC BY 4.0 . “Practice Exercises 9” is licensed under CC BY 4.0 by Thomas Edison State University.
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9. Kyoko has $10,000 that she wants to invest. Her bank has several investment accounts to choose from, all compounding daily. Her goal is to have $15,000 by the time she finishes graduate school in 6 years. To the nearest hundredth of a percent, what should her minimum annual interest rate be in order to reach her goal? (Hint: Solve the compound interest formula for the interest rate. Note: banks use 360 for n when compounded daily.) SECTION 6.2 For the following exercise, graph each set of functions on the same axes. 10. f ( x ) = 1 4 ( 3 ) x , g ( x )= 2 ( 3 ) x , h ( x )= 4 ( 3 ) x . This work, “Practice Exercises 9,” is a derivative of College Algebra 2e by Jay Abramson, OpenStax used under CC BY 4.0 . “Practice Exercises 9” is licensed under CC BY 4.0 by Thomas Edison State University.
For the following exercise, graph the function and its reflection about the x-axis on the same axes. 11. f ( x )= 3 ( 0.75 ) x 1 For the following exercise, graph the transformation of f ( x )= 2 x . Give the horizontal asymptote, the domain, and the range and describe the end behavior. 12. . f ( x )= 2 x 2 H.A. – 0.25 D: (-∞, ∞) R: (0, ∞) E.B.: f ( x ) →∞ This work, “Practice Exercises 9,” is a derivative of College Algebra 2e by Jay Abramson, OpenStax used under CC BY 4.0 . “Practice Exercises 9” is licensed under CC BY 4.0 by Thomas Edison State University.
For the following exercise, start with the graph of f ( x )= 4 x . Then write a function that results from the given transformation. 13. Reflect f ( x ) about the x axis. f ( x ) =− 4 x Numeric For the following exercise, evaluate the exponential function for the indicated value of x . 14. f ( x )= 4 ( 2 ) x 1 2, for f ( 5 ) . This work, “Practice Exercises 9,” is a derivative of College Algebra 2e by Jay Abramson, OpenStax used under CC BY 4.0 . “Practice Exercises 9” is licensed under CC BY 4.0 by Thomas Edison State University.
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Technology For the following exercise, use a graphing calculator to approximate the solution of the equation. Round to the nearest thousandth. 15. 12 = 2 ( 3 ) x + 1 . X=1.551 SECTION 6.3 Algebraic For the following exercise, rewrite the log equation in exponential form and the exponential equation in logarithmic form. 16. a) log y ( x )=− 11 b) x 10 13 = y Numeric For the following exercise, evaluate the base logarithmic expression without using a calculator. 17. log 2 ( 1 8 ) + 4 This work, “Practice Exercises 9,” is a derivative of College Algebra 2e by Jay Abramson, OpenStax used under CC BY 4.0 . “Practice Exercises 9” is licensed under CC BY 4.0 by Thomas Edison State University.
For the following exercise, evaluate the natural logarithmic expression without using a calculator. 18. ln ( e 0.225 ) 3 Real-World Applications 19. The exposure index EI for a camera is a measurement of the amount of light that hits the image receptor. It is determined by the equation EI = log 2 ( f 2 t ) where f is the “f-stop” setting on the camera, and t is the exposure time in seconds. Suppose the f-stop setting is 8 and the desired exposure time is 2 seconds. What will the resulting exposure index be? This work, “Practice Exercises 9,” is a derivative of College Algebra 2e by Jay Abramson, OpenStax used under CC BY 4.0 . “Practice Exercises 9” is licensed under CC BY 4.0 by Thomas Edison State University.
SECTION 6.4 Algebraic For the following exercise, state the domain, vertical asymptote, and end behavior of the function. 20. f ( x ) = log 3 ( 15 5 x ) + 6 E.B.: As x → ∞ ,f ( x ) ∞ , As x→∞ ,f ( x ) isundefined This work, “Practice Exercises 9,” is a derivative of College Algebra 2e by Jay Abramson, OpenStax used under CC BY 4.0 . “Practice Exercises 9” is licensed under CC BY 4.0 by Thomas Edison State University.
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Graphical For the following exercise, sketch the graphs of the pair of functions on the same axis. 21. f ( x )= log 4 ( x ) g ( x )= ln ( x ) For the following exercise, sketch the graph of the indicated function. 22. h ( x )= 1 2 ln ( x + 1 ) 3 This work, “Practice Exercises 9,” is a derivative of College Algebra 2e by Jay Abramson, OpenStax used under CC BY 4.0 . “Practice Exercises 9” is licensed under CC BY 4.0 by Thomas Edison State University.
For the following exercise, write a logarithmic equation corresponding to the graph shown. 23. Use f ( x )= log 5 ( x ) as the parent function. f ( x ) =− 2log 5 ( x ) + 5 Technology For the following exercise, use a graphing calculator to find an approximate solution to the equation. 24. 2ln ( 5 x + 1 ) = 1 2 ln ( 5 x ) + 1 x= -0.018399 x= -0.1930107 This work, “Practice Exercises 9,” is a derivative of College Algebra 2e by Jay Abramson, OpenStax used under CC BY 4.0 . “Practice Exercises 9” is licensed under CC BY 4.0 by Thomas Edison State University.