Lesson 8 Exponents and Exponential Functions Unit Review
1. Define an exponent.
An exponent is a number that represents how many times a base number is multiplied by itself.
2. What is the difference between a base and an exponent in an exponential expression?
The base is the number that is being multiplied by itself, and the exponent is the number that represents how many times the base is multiplied by itself.
3. Write the exponential expression 5^3 in expanded form.
5^3 = 5 x 5 x 5 = 125
4. What is the value of 2^4?
2^4 = 2 x 2 x 2 x 2 = 16
5. Define an exponential function.
An exponential function is a mathematical function in the form f(x) = a^x, where a is a constant and x is the variable.
6. Identify the base and exponent in the expression f(x) = 3^x.
In the expression f(x) = 3^x, the base is 3 and the exponent is x.
7. Describe the growth or decay pattern of exponential functions.
Exponential functions exhibit exponential growth or decay patterns, where the function either grows rapidly (exponential growth) or decreases rapidly (exponential decay) as the input variable increases.
8. How can you graph an exponential function?
To graph an exponential function, plot several points by choosing values for x and calculating the corresponding values of f(x) using the exponential function. Connect the points to form a smooth curve that represents the graph of the function.
9. What is the formula for compound interest, which is an example of an exponential function?
The formula for compound interest is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.