All SAT II Math I Resources
Example Questions
Example Question #1 :Solving Exponential Functions
Solve the following function:
and
and
You must getby itself so you must addto both side which results in
.
You must get the square root of both side to undue the exponent.
This leaves you with.
But since you square thein the equation, the original value you plug can also be its negative value since squaring it will make it positive anyway.
This means your answer can beor.
Example Question #2 :Solving Exponential Functions
What is the horizontal asymptote of the graph of the equation?
The asymptote of this equation can be found by observing that不管. We are thus solving for the value ofasapproaches zero.
So the value thatcannot exceed is, and the lineis the asymptote.
Example Question #1 :Solving And Graphing Exponential Equations
What is/are the asymptote(s) of the graph of the function
?
An exponential equation of the formhas only one asymptote - a horizontal one at. In the given function,, so its one and only asymptote is.
Example Question #1 :Find The Equations Of Vertical Asymptotes Of Tangent, Cosecant, Secant, And Cotangent Functions
Find the vertical asymptote of the equation.
There are no vertical asymptotes.
To find the vertical asymptotes, we set the denominator of the function equal to zero and solve.
Example Question #1 :Solving Exponential Functions
Consider the exponential function. Determine if there are any asymptotes and where they lie on the graph.
There is one vertical asymptote at.
There is one horizontal asymptote at.
There are no asymptotes.goes to positive infinity in both theanddirections.
There is one vertical asymptote at.
There is one horizontal asymptote at.
For positivevalues,increases exponentially in thedirection and goes to positive infinity, so there is no asymptote on the positive-axis. For negativevalues, asdecreases, the termbecomes closer and closer to zero soapproachesas we move along the negativeaxis. As the graph below shows, this is forms a horizontal asymptote.
Example Question #1 :Solving Exponential Functions
Solve the equation for.
Begin by recognizing that both sides of the equation have a root term of.
Using the power rule, we can set the exponents equal to each other.
Example Question #2 :Solving Exponential Functions
Solve the equation for.
Begin by recognizing that both sides of the equation have the same root term,.
We can use the power rule to combine exponents.
Set the exponents equal to each other.
Example Question #2 :Solving And Graphing Exponential Equations
In 2009, the population of fish in a pond was 1,034. In 2013, it was 1,711.
Write an exponential growth function of the formthat could be used to model, the population of fish, in terms of, the number of years since 2009.
Solve for the values ofaandb:
In 2009,and(zero years since 2009). Plug this into the exponential equation form:
.Solve forto get.
In 2013,and. Therefore,
or.Solve forto get
.
Then the exponential growth function is
.
Example Question #8 :Solving Exponential Functions
Solve for.
8 and 4 are both powers of 2.
Example Question #9 :Solving Exponential Functions
Solve for:
No solution
Because both sides of the equation have the same base, set the terms equal to each other.
Add 9 to both sides:
Then, subtract 2x from both sides:
Finally, divide both sides by 3:
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