Exam 14: Exponential and Logarithmic Functions

Express $\log b \left( x \sqrt [ 6 ] { \frac { x } { y } } \right)$ as the sum or difference of simpler logarithmic quantities. Assume that all variables represent positive real numbers.

The equation $P ( a ) = 14.7 e ^ { - 0.21 a }$ , where a is the altitude above sea level measured in miles, yields the atmospheric pressure in pounds per square inch. If the atmospheric pressure at Cheyenne, Wyoming, is approximately 11.84 pounds per square inch, find that city s altitude above sea level. Express your answer to the nearest hundred feet. Please enter your answer as a number without the units. __________ feet

In a certain balloon mortgage loan, the borrower pays the lender all of the principal and interest for the loan at the end of three years. What will be the payoff amount for a loan of $195,000 at 4% annual interest rate where the interest is compounded monthly? Please round the answer to the nearest hundredth. $__________

Use the formula $A = p e ^ { r t }$ to find the total amount of money accumulated at the end of the indicated time period by compounding continuously: $4,600 for 6 years at 3%. The choices are rounded to the nearest cent.

Find f - -1 ( x ). $f ( x ) = x ^ { 2 } + 7 \text { for } x \geq 0$

Use the formulas $A = p \left( 1 + \frac { r } { n } \right) ^ { n t }$ or $A = p _ { \mathrm { e } } r t$ to find the amount for the investments. $4,800 for 5 years at 4% compounded continuously. Please round the answer to the nearest cent. $A =$ $__________ $4,800 for 5 years at 4% compounded monthly. Please round the answer to the nearest cent. $A =$ $__________ Determine which investment amounts to more. __________

Find f -1 ( x ). $f ( x ) = - \frac { 9 } { 10 } x$

Approximate each logarithm to three decimal places. log₅2.5

Solve the equation. $\left( 2 ^ { x + 3 } \right) \left( 2 ^ { x } \right) = 4$

Suppose that in a certain culture, the equation Q ( t ) = 1,000 e ^{0.5 t} expresses the number of bacteria present as a function of the time t , where t is expressed in hours. How many bacteria are present at the end of 2 hours? The choices are rounded to the nearest whole.

Perform the following calculations and express answer to the nearest hundredth. $\frac { \log 7 } { \log 3 }$

Find the intervals on which the given function is increasing and the intervals on which it is decreasing. f ( x ) = x ² + 7

Perform the following calculations and express answer to the nearest hundredth. $\frac { \ln 9 } { 0.05 }$

Use the formula $A = p e ^ { r t }$ to find the total amount of money accumulated at the end of the indicated time period by compounding continuously: $7,250 for 12 years at 6.5%. Please round the answer to the nearest cent. $__________

Find f - -1 ( x ). $f ( x ) = \frac { 7 } { 8 } x - \frac { 6 } { 7 }$

Perform the following calculations and express answer to the nearest hundredth. $\frac { \ln 4 } { 2 \ln 2 }$

Use a calculator to find each common logarithm. Express answer to four decimal places. $\log 0.00076$

Solve the equation. $\left( 256 ^ { x } \right) \left( 4 ^ { 12 x - 1 } \right) = 64$

Form the inverse function f ^{- -1}, and list the domain and range of f ^{- -1}. f = {(1, 6), (4, 8), (6, 50)} Match the name of each set with the corresponding set. - $\{ 1,4,6 \}$

Perform the following calculations and express answer to the nearest hundredth. $\frac { 4 \ln 6 } { \ln 5 }$