Exponential Functions Review

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

Identify the characteristics of exponential growth.

Back

Exponential growth occurs when the growth rate of a value is proportional to its current value, leading to rapid increases over time. The base 'b' in f(x) = a * b^x is greater than 1.

Front

Identify the characteristics of exponential decay.

Back

Exponential decay occurs when the growth rate of a value is proportional to its current value, leading to rapid decreases over time. The base 'b' in f(x) = a * b^x is between 0 and 1.

Front

What is the y-intercept of an exponential function?

Back

The y-intercept of an exponential function f(x) = a * b^x is the value of f(0), which equals 'a'.

Front

How do you determine if an exponential function represents growth or decay?

Back

If the base 'b' is greater than 1, the function represents growth. If 'b' is between 0 and 1, it represents decay.

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 interest is compounded per year, and t is the number of years.

Front

What does the term 'common ratio' refer to in exponential functions?

Back

The common ratio (b) in an exponential function f(x) = a * b^x is the factor by which the function's value multiplies for each unit increase in x.

Front

How do you find the total amount paid on a loan with compound interest?

Back

To find the total amount paid on a loan with compound interest, use the formula A = P(1 + r/n)^(nt) and calculate the total amount A after the specified time.

Front

What is the difference between linear and exponential functions?

Back

Linear functions have a constant rate of change, while exponential functions have a variable rate of change that increases or decreases rapidly.

Front

What is the significance of the base in an exponential function?

Back

The base determines the rate of growth or decay. A base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.