The Number e: 동영상 및 연습문제

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

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

2^√3

In the given equation, solve for x.

(2/11)^x = 14641/16

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

e^{- 1.9}

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.

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

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

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

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

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

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}

Plot the given function on the rectangular coordinate system.

f(x) = 15^x

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

Plot the given function on the rectangular coordinate system.

f(x) = (1/30)^-x

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

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^-5x

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

Provide the domain and range of the function by graphing it.

f(x) = 11^{x +3} +27

Provide the domain and range of the function by graphing it.

f(x) = (1/11)^{x +7}

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?

Provide the domain and range of the function by graphing it.

f(x) = -(1/11)^x-7 +5

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

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

Solve for x in the given equation.

(13/7)^x = 49/169

Solve for x in the given equation.

x^3/2 = 4913

Solve for x in the given equation.

(1/e)^-3x = (1/e³)^2x+5

Simplify $e^3\times e^{-8}$ to a single power of $e$.

Compute $e^{1.2}$. Round to the nearest hundredth.

For $f\left(x\right)=e^x$, determine the $y$-value of the horizontal asymptote.

Find the $x$-intercept of $g\left(x\right)=2-e^{x-1}$. Round to the nearest hundredth.