Exponents and exponential functions unit test
The unit test for exponents and exponential functions may include the following types of questions:
1. Multiple choice: Determine the value of a given exponential expression, such as 2^3 or 5^-2.
Example: What is the value of 3^4?
a) 27
b) 81
c) 12
d) 6
2. Short answer: Write an exponent in expanded form, such as 2^3 = 2 * 2 * 2.
Example: Expand the exponent: 4^2 = ____________
3. True or false: Determine if a given statement about exponents or exponential functions is true or false.
Example: The exponential function f(x) = 2^x is always increasing.
a) True
b) False
4. Problem solving: Solve word problems involving exponential growth or decay.
Example: A bacteria population grows exponentially. After 4 hours, there are 1000 bacteria, and after 6 hours, there are 4000 bacteria. What is the growth rate per hour?
5. Graphing: Interpret and analyze graphs of exponential functions.
Example: The graph below represents an exponential function. What is the asymptote in this graph?
^
|
| * *
| * *
| **
| *
| *
+------------------------------------------------
0 5 10 15 20 25 30 35 40 X-axis
6. Multiple choice: Determine the equation of an exponential function given certain conditions.
Example: What is the equation of an exponential function that has an initial value of 4 and a growth factor of 2?
a) f(x) = 2^x + 4
b) f(x) = 4 * 2^x
c) f(x) = 2x + 4
d) f(x) = 4x^2
These are just a few examples of the types of questions that may be included in the unit test for exponents and exponential functions. It is important to review the concepts thoroughly and practice various types of problems to prepare for the test.