Question 1

Graph the exponential function. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Graph the exponential function. 
A) 
B) 
C)...

Question 2

Find the graph of the function. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the graph of the function. 
A)...

Question 3

Write the equation  in logarithmic form.
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Write the equation  in logarithmic form.
A)...

Question 4

Simplify the expression. 
A)4
B)5
C)20
D)16
E)none of these

Accepted Answer

The answer of Simplify the expression. 
A)4
B)5
C)20
D)16
E)none of these...

Question 5

Graph the function using translations. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Graph the function using translations. 
A) 
B)...

Question 6

Assume that x is a positive number. Use the properties of logarithms to write the expression  as the logarithm of one quantity.
A) 
B) 
C) 
D) 
E)

Accepted Answer

Using the property of logarithms, we can write the given expression as:

$$e^{11eb80b1_b036_cc85_a291_5794c7ec63fd_TB8633_11} = x$$

Taking the natural logarithm of both sides, we get:

$$\ln(e^{11eb80b1_b036_cc85_a291_5794c7ec63fd_TB8633_11}) = \ln(x)$$

Using the property $\ln(e^y) = y$, we can simplify the left-hand side:

$$11eb80b1_b036_cc85_a291_5794c7ec63fd_TB8633_11 = \ln(x)$$

Therefore, the given expression is equivalent to the logarithm $11eb80b1_b036_cc85_a291_5794c7ec63fd_TB8633_11$ of the quantity $x$. Choice D matches this result.

Question 7

Use a calculator to find the value for  to four decimal places.
A)-0.1497
B)-0.3449
C)0.8502
D)-0.8502
E)0.1497

Accepted Answer

The answer of Use a calculator to find the value...

Question 8

Solve the equation. 2^x = 7 A)x = 1.3562 B)x = 1.5907 C)x = 0.3562 D)x = 5.7883 E)x = 0.4796

Accepted Answer

The answer of Solve the equation. 2^x = 7 A)x =...

Question 9

Graph the function using translations. 
A) 
B) 
C) 
D)

Accepted Answer

Translations involve shifting the graph of a function horizontally, vertically, or both. None of the answer choices provide the original function to be translated, so we cannot determine the exact translation. However, looking at the options, choice C appears to have a slight shift upwards compared to the other options.

Question 10

Find the value of b, if any, that would cause the graph of  to look like the graph shown. 
A)b = 3.7
B)b = 4.3
C)b = 1
D)b = 4
E)b = 3

Accepted Answer

The graph shows a horizontal asymptote at y = 4, which means that the exponential function approaches 4 as x approaches infinity or negative infinity. The only value of b that would create this graph is 4.

Question 11

Find the value of b that would cause the graph of y = b^x to look like the graph below. A) B) C) D) E)

Accepted Answer

By comparing the given graph with the equation y = b^x we can infer the following: 1. The function has a horizontal asymptote at y = 4. This means that b must be equal to 4. 2. The function has a vertical asymptote at x = 2. This means that the denominator of the rational function must be (x - 2). Putting these two conditions together, the equation becomes: y = 4^x / (x - 2) Simplifying this expression, we get: y = 4 / (2 - x) This is the equation of a vertical line passing through x = 2 with a y-intercept of 4. Thus, the correct choice is C, 11eb80b1_b03b_aeb5_a291_47bad4a51109_TB8633_11.

Question 12

Graph the function. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Graph the function. 
A) 
B) 
C) 
D)...

Question 13

Find the value of x. 
A)x = 65,536
B)x = 32,768
C)x = 4
D)x = 8

Accepted Answer

The answer of Find the value of x. 
A)x =...

Question 14

Tritium, a radioactive isotope of hydrogen, has a half-life of 12.4 years. Of an initial sample of 60 grams, how much will remain after 81 years?
A)2.8307 grams
B)0.6483 grams
C)15.0000 grams
D)53.9595 grams
E)0.0000 grams

Accepted Answer

We can use the formula:
(amount remaining) = (initial amount) x (1/2)^(time elapsed/half-life)
Plugging in the values:
(amount remaining) = 60 x (1/2)^(81/12.4)
(amount remaining) = 0.6483 grams

Question 15

Find the value of b that would cause the graph of y = b^x to look like the graph indicated. A) B) C) D) E)

Accepted Answer

The answer of Find the value of b that would...

Question 16

Identify the graph of the function. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Identify the graph of the function. 
A)...

Question 17

Assume that x, y, and z are positive numbers. Use the properties of logarithms to write the expression  as the logarithm of one quantity.
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Assume that x, y, and z are...

Question 18

Use a graphing utility to determine which graph below is the graph of the function. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Use a graphing utility to determine which...

Question 19

Graph the function using translations. 
A) 
B) 
C) 
D)

Accepted Answer

The function has been translated 3 units to the left and 2 units down. Choice A translates the function 3 units to the right, choice B translates the function 2 units up, and choice D translates the function 4 units to the right and 3 units up, which does not match the given translations. Therefore, choice C is the best option.

Question 20

Find the graph of the function. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the graph of the function. 
A)...

Quiz 4: Exponential and Logarithmic Functions

Graph the exponential function.

Find the graph of the function.

Write the equation in logarithmic form.

Simplify the expression.

Graph the function using translations.

Assume that x is a positive number. Use the properties of logarithms to write the expression as the logarithm of one quantity.

Use a calculator to find the value for to four decimal places.

Solve the equation. 2x = 7

Graph the function using translations.

Find the value of b, if any, that would cause the graph of to look like the graph shown.

Find the value of b that would cause the graph of y = bx to look like the graph below.

Graph the function.

Find the value of x.

Tritium, a radioactive isotope of hydrogen, has a half-life of 12.4 years. Of an initial sample of 60 grams, how much will remain after 81 years?

Find the value of b that would cause the graph of y = bx to look like the graph indicated.

Identify the graph of the function.

Assume that x, y, and z are positive numbers. Use the properties of logarithms to write the expression as the logarithm of one quantity.

Use a graphing utility to determine which graph below is the graph of the function.

Graph the function using translations.

Find the graph of the function.

Solve the equation. 2^x = 7

Find the value of b that would cause the graph of y = b^x to look like the graph below.

Find the value of b that would cause the graph of y = b^x to look like the graph indicated.