All Precalculus Resources
Example Questions
Example Question #1 : Solve Exponential Equations
Solve:
None of the other answers.
Combine the constants:
Isolate the exponential function by dividing:
Take the natural log of both sides:
Finally isolate x:
Example Question #2 : Solve Exponential Equations
Solve the equation for .
The key to this is that . From here, the equation can be factored as if it were .
and
and
and
Now take the natural log (ln) of the two equations.
and
and
Example Question #1 : Graph Exponential Functions
Choose the description below that matches the equation:
Exponential growth
Y-intercept at
Exponential decay
Y-intercept at
Exponential growth
Y-intercept at
Exponential growth
Y-intercept at
Exponential decay
Y-intercept at
Exponential growth
Y-intercept at
Exponential graphs can either decay or grow. This is based on the value of the base of the exponent. If the base is greater than , the graph will be growth. And, if the base is less than , then the graph will be decay. In this situation, our base is . Since this is greater than , we have a growth graph. Then, to determine the y-intercept we substitute . Thus, we get:
for the y-intercept.
Example Question #2 : Graph Exponential Functions
Choose the description that matches the equation below:
Exponential growth
Exponential growth
Exponential decay
Exponential decay
Exponential decay
Exponential decay
Exponential graphs can either decay or grow. This is based on the value of the base of the exponent. If the base is greater than , the graph will be growth. And, if the base is less than , then the graph will be decay. In this situation, our base is . Since this is less than , we have a decay graph. Then, to determine the y-intercept we substitute . Thus, we get:
for the y-intercept.
Example Question #1 : Graph Exponential Functions
Which of the following represents the graph of ?
Note that the negative sign in this function comes outside of the parentheses. This should show you that the bigger the number in parentheses, the lower the curve of the graph will go. Since this is an exponential function, the larger that the x value gets, then, the "more negative" this graph will go. The graph closest to zero on the left-hand side - where x is negative - and then shoots down and to the right rapidly when x gets larger is the correct graph.
Example Question #984 : Problem Solving Questions
Define a function as follows:
Give the -intercept of the graph of .
The -coordinate ofthe -intercept of the graph of is 0, and its -coordinate is :
The -intercept is the point .
Example Question #122 : Solving And Graphing Exponential Equations
Does the function have any -intercepts?
Yes,
No
Yes, and
Yes,
That cannot be determined from the information given.
No
The -intercept of a function is where . Thus, we are looking for the -value which makes .
If we try to solve this equation for we get an error.
To bring the exponent down we will need to take the natural log of both sides.
Since the natural log of zero does not exist, there is no exponent which makes this equation true.
Thus, there is no -intercept for this function.
Example Question #21 : Solving Exponential Functions
Which of the following functions represents exponential decay?
Exponential decay describes a function that decreases by a factor every time increases by .
These can be recognizable by those functions with a base which is between and .
The general equation for exponential decay is,
where the base is represented by and .
Thus, we are looking for a fractional base.
The only function that has a fractional base is,
.
Example Question #2 : Graph Exponential Functions
What is the -intercept of ?
There is no -intercept.
The -intercept of a graph is the point on the graph where the -value is .
Thus, to find the -intercept, substitute and solve for .
Thus, we get: