Exponential Functions and Graphs

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 a positive real number, and 'x' is the exponent.

Front

What happens to the value of an exponential function as 'x' increases?

Back

As 'x' increases, the value of the exponential function increases rapidly if 'b' > 1, or decreases rapidly if '0 < b < 1.

Front

What is the base in an exponential function?

Back

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

Front

If you start with $10 and it doubles every year, how much will you have after 3 years?

Back

$80.

Front

What is the general shape of the graph of an exponential function with a base greater than 1?

Back

The graph rises steeply to the right and approaches the x-axis to the left.

Front

What is the y-intercept of the exponential function f(x) = 2^x?

Back

The y-intercept is (0, 1) because f(0) = 2^0 = 1.

Front

What does it mean for a function to be exponential growth?

Back

Exponential growth occurs when the growth rate of a value is proportional to its current value, leading to rapid increases.

Front

What does it mean for a function to be exponential decay?

Back

Exponential decay occurs when the value decreases at a rate proportional to its current value, leading to rapid decreases.

Front

How do you find the value of an exponential function at a specific point?

Back

Substitute the value of 'x' into the function f(x) = a * b^x and calculate.

Front

What is the equation of an exponential function that doubles every year?

Back

f(x) = a * 2^x, where 'a' is the initial amount.