Table of contents

0. Review of Algebra(0)
1. Equations & Inequalities(0)
2. Graphs of Equations(0)
3. Functions(0)
4. Polynomial Functions(0)
5. Rational Functions(0)
6. Exponential & Logarithmic Functions(0)
7. Systems of Equations & Matrices(0)
8. Conic Sections(0)
9. Sequences, Series, & Induction(0)
10. Combinatorics & Probability(0)

6. Exponential & Logarithmic Functions

The Number e

6. Exponential & Logarithmic Functions

The Number e - Online Tutor, Practice Problems & Exam Prep

The Number e Practice Problems

26 problems

1PRACTICE PROBLEM

The graph of an exponential function is shown. Which of the following function represents the graph?

2PRACTICE PROBLEM

Use a calculator to approximate the value of the following number to six decimal places.

2^√3

3PRACTICE PROBLEM

In the given equation, solve for x.
(2/11)^x = 14641/16

4PRACTICE PROBLEM

Use a calculator to approximate the value of the following number to four decimal places.

e^{- 1.9}

5PRACTICE PROBLEM

Consider the functions f(x) = e^x and g(x) = 4e^x/2. Apply transformations on the graph of f in constructing the graph of g. Graph the asymptotes and identify their equations. Then, use the graph to determine the domain and range of both functions.

6PRACTICE PROBLEM

Determine f(-1) for f(x) = 15^x. Approximate the answer to the nearest thousandth if required.

7PRACTICE PROBLEM

Graph the following function by constructing a table of values. You may use a graphing utility to check your graph: f(x) = (1/4)^x

8PRACTICE PROBLEM

Determine f(-1/2) for f(x) = 15^x. Approximate the answer to the nearest thousandth if required.

9PRACTICE PROBLEM

An exponential function's graph is presented. From the list of available functions, pick one for the graph.

10PRACTICE PROBLEM

Determine f(-0.59) for f(x) = 15^x. Approximate the answer to the nearest thousandth if required.

11PRACTICE PROBLEM

Graph f(x) = 10^x to start. After that, graph the provided function using transformations of this graph. Graph the asymptotes and provide equations. Find the function's domain and range using the graphs.
g(x) = 10^{x -9}

12PRACTICE PROBLEM

Plot the given function on the rectangular coordinate system.
f(x) = 15^x

13PRACTICE PROBLEM

Graph f(x) = 7^x to start. After that, graph the provided function using transformations of this graph. Graph the asymptotes and provide equations. Find the function's domain and range using the graphs.
g(x) = 7∙7^x

14PRACTICE PROBLEM

Plot the given function on the rectangular coordinate system.
f(x) = (1/30)^-x

15PRACTICE PROBLEM

The graph of f(x) = e^x is shown in the figure. To graph the given function, use the transformations of this graph. Give the asymptotes' equations. Find the domain and range of the function using the graphs.
g(x) = e^x -8

16PRACTICE PROBLEM

17PRACTICE PROBLEM

Use the same rectangular coordinate system to show the graphs of functions f and g. For every asymptote, graph it and provide the equations.
f(x) = 24^x and g(x) = 24^-x

18PRACTICE PROBLEM

Provide the domain and range of the function by graphing it.
f(x) = 11^{x +3} +27

19PRACTICE PROBLEM

Provide the domain and range of the function by graphing it.
f(x) = (1/11)^{x +7}

20PRACTICE PROBLEM

Use the compound interest formula A = P(1 + r/n)^nt to solve the problem. If $8000 is deposited to an account with an interest rate of 1.18% compounded monthly, what is its value after 10 years?

21PRACTICE PROBLEM

Provide the domain and range of the function by graphing it.
f(x) = -(1/11)^x-7 +5

22PRACTICE PROBLEM

Which of the following exponential functions represent the graph given below?