Exam 4: Exponential and Logarithmic Functions

Graph the function using a graphing utility and the Change-of-Base Formula. - $\log _ { x } - 5 ( x + 5 )$ A) B) C) D)

Find the exact value of the logarithmic expression. - $\log _ { 9 } \frac { 1 } { 729 }$

Solve the equation. - $4 ^ { - x } = \frac { 1 } { 16 }$

Solve the problem. -Bob, the incredible shrinking man, loses half of his height each day after he was exposed to a mysterious form of cosmic radiation. How many days before he is literally "knee-high to a grasshopper"? Assume that a grasshopper's knee is 4 millimeters high and that Bob is 2 meters tall. Round your answer to the nearest whole day. (1000 millimeters = 1 meter)

Find the effective rate of interest. -12.25% compounded monthly

Solve the exponential equation. Express the solution set in terms of natural logarithms. - $6 ^ { 8 x } = 2.2$

Find the amount that results from the investment. -$14,000 invested at 15% compounded semiannually after a period of 9 years

Find the inverse function of f. State the domain and range of f. - $f ( x ) = \frac { 3 x - 2 } { x + 5 }$

Solve the equation. - $\mathrm { e } ^ { 3 \mathrm { x } } = 5$

Express as a single logarithm. - $3 \log _ { \mathrm { b } } \mathrm { q } - \log _ { \mathrm { b } } \mathrm { r }$

The function f is one-to-one. Find its inverse. - $f ( x ) = 3 x + 4$

Decide whether the composite functions, f $f \circ g$ nd $\mathbf { g } \circ \mathrm { f }$ f, are equal to x. - $f ( x ) = \sqrt [ 5 ] { x - 8 } , g ( x ) = x ^ { 5 } + 8$

Solve the problem. -A thermometer reading 11°C is brought into a room with a constant temperature of 30°C. If the thermometer reads 17°C after 4 minutes, what will it read after being in the room for 7 minutes? Assume the cooling follows Newton's Law of Cooling: $\mathrm { U } = \mathrm { T } + \left( \mathrm { U } _ { \mathrm { O } } - \mathrm { T } \right) \mathrm { e } ^ { \mathrm { kt } }$ (Round your answer to two decimal places.)

Graph the function. - $f ( x ) = 5 ^{( x - 1 )} - 2$ A) B) C) D)

The Richter scale converts seismographic readings into numbers for measuring the magnitude of an earthquake according to this function $M ( x ) = \log \left( \frac { x } { x _ { 0 } } \right) , \text { where } x _ { 0 } = 10 ^ { - 3 }$ -Find the magnitude (to one decimal place) of an earthquake whose seismographic reading is 2000 millimeters at a distance of 100 kilometers from its epicenter.

Change the logarithmic expression to an equivalent expression involving an exponent. - $\log _ { \sqrt { 3 } } 64 = \frac { 7 } { 11 }$

Solve the problem. -The value of a particular investment follows a pattern of exponential growth. In the year 2000, you invested money in a money market account. The value of your investment t years after 2000 is given by the exponential Growth model A $\mathrm { A } = 5,300 \mathrm { e } ^ { 0.045 \mathrm { t } }$ . How much did you initially invest in the account?

The graph of a one-to-one function f is given. Draw the graph of the inverse function f-1 as a dashed line or curve. - $f(x)=2 x$ A) B)

Use a graphing calculator to solve the equation. Round your answer to two decimal places. - $e ^ { x } = x ^ { 3 }$

Find the domain of the function. - $f ( x ) = \ln \left( 6 x - x ^ { 2 } \right)$