Exponential Functions

Front

What is an exponential function?

Back

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

Front

What does the base of an exponential function indicate?

Back

The base of an exponential function indicates the growth or decay factor. If the base is greater than 1, the function represents exponential growth; if the base is between 0 and 1, it represents exponential decay.

Front

Identify the y-intercept of the function y = 5(3)^x.

Back

The y-intercept is (0, 5). This is found by evaluating the function at x = 0.

Front

What is the rate of growth in the function y = 2(1.7)^x?

Back

The rate of growth is 70%, which is calculated as (1.7 - 1) * 100%.

Front

How do you determine if a function is exponential growth or decay?

Back

If the base of the exponential function is greater than 1, it is exponential growth. If the base is between 0 and 1, it is exponential decay.

Front

What is the general form of an exponential decay function?

Back

The general form of an exponential decay function is y = a(b)^x, where 0 < b < 1.

Front

What is the y-intercept of the function y = 13(0.27)^x?

Back

The y-intercept is (0, 13). This is found by evaluating the function at x = 0.

Front

What does the term 'exponential decay' mean?

Back

Exponential decay refers to a decrease in quantity at a rate proportional to its current value, resulting in a rapid decline.

Front

What is the effect of changing the base in an exponential function?

Back

Changing the base affects the rate of growth or decay. A larger base results in faster growth, while a smaller base (between 0 and 1) results in faster decay.

Front

How can you graph an exponential function?

Back

To graph an exponential function, plot the y-intercept, calculate additional points by substituting values for x, and draw a smooth curve through the points.