Review - Exponential Functions and Their Properties

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a * b^x, where 'a' is a constant, 'b' is the base (a positive real number), and 'x' is the exponent.

Front

What does it mean for interest to be compounded semi-annually?

Back

Compounding semi-annually means that the interest is calculated and added to the principal twice a year.

Front

What is the formula for compound interest?

Back

The formula for compound interest is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the number of years.

Front

What is exponential decay?

Back

Exponential decay describes a process where a quantity decreases at a rate proportional to its current value, often represented by the function f(t) = a * e^(-kt), where 'k' is a positive constant.

Front

What is the difference between exponential growth and decay?

Back

Exponential growth occurs when a quantity increases over time, while exponential decay occurs when a quantity decreases over time.

Front

How do you solve an exponential equation?

Back

To solve an exponential equation, you can take the logarithm of both sides or rewrite the equation in a form that allows you to isolate the variable.

Front

What is the value of 4^(-2)?

Back

4^(-2) = 1/(4^2) = 1/16.

Front

If 4^(3b - 3) = 1/16, what is b?

Back

b = 1/3.

Front

If 4^(p + 2) = 64, what is p?

Back

p = 1.

Front

What is the base of an exponential function?

Back

The base of an exponential function is the constant 'b' in the function f(x) = a * b^x, which determines the rate of growth or decay.