Exponential Functions

Front

What is an exponential function?

Back

A function of the form y = a(b)^x, where a is a constant, b is a positive real number, and x is the exponent.

Front

What distinguishes exponential growth from exponential decay?

Back

Exponential growth occurs when the base (b) is greater than 1, while exponential decay occurs when the base (b) is between 0 and 1.

Front

What is the general form of an exponential function?

Back

y = a(b)^x, where a is the initial value, b is the growth/decay factor, and x is the exponent.

Front

If a function triples each year, what type of function is it?

Back

Exponential function.

Front

What is the y-intercept of an exponential function y = a(b)^x?

Back

The y-intercept is the value of y when x = 0, which is y = a.

Front

What is the base of an exponential function?

Back

The base (b) is the constant that is raised to the power of x in the function y = a(b)^x.

Front

What does it mean for a function to have a constant rate of change?

Back

It means the function is linear, as it adds or subtracts the same value for each unit increase in x.

Front

What is the difference between linear and exponential growth?

Back

Linear growth adds a constant amount, while exponential growth increases by a constant percentage.

Front

What is the formula for calculating exponential growth?

Back

y = a(1 + r)^t, where r is the growth rate and t is time.

Front

What is the formula for calculating exponential decay?

Back

y = a(1 - r)^t, where r is the decay rate and t is time.