# Section 4.1 inverse function 6. decide whether each function as

SECTION 4.1 INVERSE FUNCTION

6. Decide whether each function as graphed or defined is one-to-one. (SEE PICTURE) P.394

12. Decide whether each function as graphed or defined is one-to-one

16. Decide whether each function as graphed or defined is one-to-one

42. Use the definition of inverses to determine whether f and g are inverses.

60*.

68*.(SAME FOR THIS QUESTIONS AS LISTED IN #60)

SECTION 4.2 EXPONENTIAL FUNCTIONS

20*. Graph the function:

28*. Graph the function :

64. Solve the equation:

80. Solve the equation:

88(a) Find the future value and interest earned if $56,780 is invested at 5.3% compounded

quarterly for 23 quarters.

92. Find the required annual interest rate to the nearest tenth of a percent for $65,000 to grow to

$65,325 if interest is compounded monthly for 6 months.

SECTION 4.3 LOGARITHMIC FUNCTIONS

4. If the statement is in exponential form, write it in an equivalent logarithmic form. If the

statement is in logarithmic form, write it in exponential form.

10. If the statement is in exponential form, write it in an equivalent logarithmic form. If the

statement is in logarithmic form, write it in exponential form

14. Solve the logarithmic equation.

28. Solve the logarithmic equation

66. Use the properties of logarithms to rewrite each expression. Simplify the result if possible.

Assume all variables represent positive real numbers.

90. Given the approximations , find each logarithm without using a calculator.

SECTION 4.4 EVALUATING LOGARITHMS AND THE CHANGE-OF-BASE

THEOREM

12. Find each value. If applicable, give an approximation to four decimal places.

14. Find each value. If applicable, give an approximation to four decimal places.

18. Find each value. If applicable, give an approximation to four decimal places.

66. On December 26, 2004, an earthquake struck in the Indian Ocean with a magnitude of 9.1 on

the Richter scale. The resulting tsunami killed an estimated 229,900 people in several countries.

Express this reading in ters of

80. Use the change-of-base theorem to find an approximation to four decimal places for the

logarithm.

SECTION 4.5 EXPONENTIAL AND LOGARITHMS EQUATIONS

8. Solve each exponential equation. Express irrational solutions as decimals correct to the nearest

thousandth. Express solutions in exact form.

24. Solve each exponential equation. Express irrational solutions as decimals correct to the

nearest thousandth. Express solutions in exact form. =7

38. Solve logarithmic equation. Express all solutions in exact form.

96. Find t to the nearest hundredth of a year if $1786 becomes $2063 at 2.6%, with interest

compounded monthly.

98. At what interest rate, to the nearest hundredth of a percent, will $16,000 grow to $20,000 if

invested for 5.25yr and interest is compounded quarterly?

SECTION 4.6 APPLICATIONS AND MODELS OF EXPONENTIAL GROWTH AND

DECAY

18. A sample from a refuse deposit near the Strait of Magellan had 60% of the carbon-14 of a

contemporary sample. How old was the sample?

20. The amount of a chemical that will dissolve in a solution increases exponentially as the

(Celsius) temperature t is increased according to the model

At what temperature will 15g dissolve?

26. If Russ chooses the plan with continuous compounding, how long will it take for his $60,000

to grow to $80,000?

28. If interest is compounded continuously and the interest rate is tripled, what effect will this

have on the time required for an investment to double?

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