SAT II Math I : Solving Exponential Functions
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Example Questions
Example Question #31 : Solving Exponential Functions
Which of the following correctly describes the graph of an exponential function with a base of three?
It stays constant.
It begins by decreasing quickly and then levels out.
It begins by decreasing gradually and then decreases more quickly.
It starts out by gradually increasing and then increases faster and faster.
It starts by increasing quickly and then levels out.
It starts out by gradually increasing and then increases faster and faster.
Exponential functions with a base greater than one are models of exponential growth. Thus, we know that our function will increase and not decrease. Remembering the graph of an exponential function, we can determine that the graph will begin gradually, almost like a flat line. Then, as 
Example Question #81 : Functions And Graphs
Solve:
The base of the right side can be rewritten as base two.
Simplify the equation.
Add 
Subtract 3 on both sides.
Divide by 20 on both sides.
The answer is:
Example Question #31 : Solving Functions
Solve:
To solve, change the base of the fraction to base 4.
With similar bases, we can set the powers equal.
Add one on both sides.
Divide by 2 on both sides.
The answer is 
Example Question #81 : Functions And Graphs
Solve:
Rewrite the right side as base 2.
Replace the term into the equation.
With similar bases, we can set the exponents equal.
Subtract six from both sides.
Divide by negative three on both sides.
The answer is:
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