Exam 9: Exponential and Logarithmic Functions

An account now contains $11,160 and has been accumulating interest at 7.2% annual interest, compounded continuously, for 7 years. Find the initial deposit.

Solve the equation. Round answer to four decimal places. $7 ^ { x } = 14$

If $450 is deposited in an account paying 8.6% annual interest, compounded semiannually, how long will it take for the account to increase to $800? Please round the answer to the nearest tenth.

The function $f ( x ) = e ^ { x }$ is graphed and the TRACE feature is used. What is the y -coordinate of the point on the graph having an x-coordinate of 1? What is the symbol that represents this number? The $y$ -coordinate (to seven decimal places) is __________. It is named __________.

Write the logarithm as a sum and/or difference of logarithms of a single quantity. Then simplify, if possible. Assume that d , f and b are positive numbers, and $\log _ { 5 } 9$ . $\log _ { b } 7 = 0.8451$

Solve: $\log x + \log ( x - 15 ) = 2$

Solve for x . $\log _ { 81 } x = - \frac { 1 } { 2 }$

Refer to the graph of $f ( x ) = 2 ^ { x }$ . What is the domain of the function? Please enter your answer in interval notation.

The hydrogen ion concentration of sour pickles is $6.91 \times 10 ^ { - 5 }$ . Find the pH. Round the answer to the nearest tenth.

An initial deposit of $20,000 earns 3% interest, compounded monthly. How much will be in the account after 15 years? Round your answer to the nearest cent.

Base 10 logarithms are called _________ logarithms.

Solve: $\log _ { 6 } x = 0$

Assume that $\log _ { 5 } 9$ and $\log _ { b } 7 = 0.8451$ . Use these values to evaluate the logarithm. $\log _ { b } 9 = 0.9542$

An equation with a logarithmic expression that contains a variable, such as $\log _ { 5 } ( 2 x - 7 ) = \log _ { 5 } ( x + 1 )$ , is a(n) __________ equation.

Solve the equation. $4 ^ { x ^ { 2 } + 4 x } = \frac { 1 } { 256 }$ If there is more than one solution, separate your answers with commas.

Let $f ( x ) = 4 x - 3$ and $g ( x ) = x ^ { 2 } + x$ . Find the composition. $( g \circ f ) ( - 3 )$

What is the formula for exponential growth/decay? (Let P be a quantity that increases or decreases at annual rate r , compounded continuously, and A the amount after t years.)

$f ( x ) = \ln x$ is called the __________ logarithmic function. The base is __________.

If the point (7,-4) is on the graph of the one-to-one function f , then the point __________ is on the graph of $f ^ { - 1 }$ .

Write the logarithm as a sum and/or difference of logarithms of a single quantity. Then simplify, if possible. Assume that w , r and b are positive numbers, and $b \neq 1$ . $\log _ { b } \sqrt [ 5 ] { w r }$