Question 1

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.

Accepted Answer

The answer of An account now contains $11,160 and has...

Question 2

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

Accepted Answer

The answer of Solve the equation. Round answer to four...

Question 3

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.

Accepted Answer

The answer of If $450 is deposited in an account...

Question 4

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 __________.

Accepted Answer

The answer of The function \(f ( x ) =...

Question 5

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 $\log _ { 5 } 9$ . $\log _ { b } 7 = 0.8451$

Accepted Answer

The answer of Write the logarithm as a sum and/or...

Question 6

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

Accepted Answer

A)  $\left\{ \frac { 500 } { 33 } \right\}$ 
B)  no solution 
C)  $\{ - 5 \}$ 
D)  $\{ 20 \}$

Question 7

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

Accepted Answer

The answer of Solve for x . \(\log _ {...

Question 8

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

Accepted Answer

The answer of Refer to the graph of \(f (...

Question 9

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

Accepted Answer

The answer of The hydrogen ion concentration of sour pickles...

Question 10

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.

Accepted Answer

A)  $4,090,067.19 
B)  $31,348.63 
C)  $31,159.35 
D)  $20,763.27

Question 11

Base 10 logarithms are called _________ logarithms.

Accepted Answer

The answer of Base 10 logarithms are called _________ logarithms....

Question 12

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

Accepted Answer

A)  0 
B)  6 
C)  5 
D)  1

Question 13

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

Accepted Answer

The answer of Assume that \(\log _ { 5 }...

Question 14

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.

Accepted Answer

The answer of An equation with a logarithmic expression that...

Question 15

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

Accepted Answer

The answer of Solve the equation. \(4 ^ { x...

Question 16

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

Accepted Answer

The answer of Let \(f ( x ) = 4...

Question 17

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.)

Accepted Answer

The answer of What is the formula for exponential growth/decay?
...

Question 18

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

Accepted Answer

The answer of $f ( x ) = \ln x$...

Question 19

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

Accepted Answer

The answer of If the point (7,-4) is on the...

Question 20

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 $b \neq 1$ . $\log _ { b } \sqrt [ 5 ] { w r }$

Accepted Answer

The answer of Write the logarithm as a sum and/or...

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.

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 $f ( x ) = 2 ^ { x }$ . $Refer to the graph of f ( x ) = 2 ^ { x } . What is the domain of the function? Please enter your answer in interval notation.$ 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 $b \neq 1$ . $\log _ { b } \sqrt [ 5 ] { w r }$

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. 7x=147 ^ { x } = 147x=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.

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⁡59\log _ { 5 } 9log5​9 . log⁡b7=0.8451\log _ { b } 7 = 0.8451logb​7=0.8451

Solve: log⁡x+log⁡(x−15) =2\log x + \log ( x - 15 ) = 2logx+log(x−15) =2

Solve for x . log⁡81x=−12\log _ { 81 } x = - \frac { 1 } { 2 }log81​x=−21​

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

The hydrogen ion concentration of sour pickles is 6.91×10−56.91 \times 10 ^ { - 5 }6.91×10−5 . 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⁡6x=0\log _ { 6 } x = 0log6​x=0

Assume that log⁡59\log _ { 5 } 9log5​9 and log⁡b7=0.8451\log _ { b } 7 = 0.8451logb​7=0.8451 . Use these values to evaluate the logarithm. log⁡b9=0.9542\log _ { b } 9 = 0.9542logb​9=0.9542

An equation with a logarithmic expression that contains a variable, such as log⁡5(2x−7)=log⁡5(x+1)\log _ { 5 } ( 2 x - 7 ) = \log _ { 5 } ( x + 1 )log5​(2x−7)=log5​(x+1) , is a(n) __________ equation.

Solve the equation. 4x2+4x=12564 ^ { x ^ { 2 } + 4 x } = \frac { 1 } { 256 }4x2+4x=2561​ If there is more than one solution, separate your answers with commas.

Let f(x)=4x−3f ( x ) = 4 x - 3f(x)=4x−3 and g(x)=x2+xg ( x ) = x ^ { 2 } + xg(x)=x2+x . Find the composition. (g∘f)(−3)( g \circ f ) ( - 3 )(g∘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⁡xf ( x ) = \ln xf(x)=lnx 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−1f ^ { - 1 }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≠1b \neq 1b=1 . log⁡bwr5\log _ { b } \sqrt [ 5 ] { w r }logb​5wr​

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

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

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. $( g \circ f ) ( - 3 )$

$f ( x ) = \ln x$ 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 $b \neq 1$ . $\log _ { b } \sqrt [ 5 ] { w r }$