Key Features of Exponential Functions

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 the 'a' represent in the function f(x) = a(b)^x?

Back

'a' represents the initial value or y-intercept of the exponential function.

Front

How do you find the y-intercept of an exponential function?

Back

To find the y-intercept, evaluate the function at x = 0. This gives f(0) = a(b)^0 = a.

Front

What is the growth factor in an exponential function?

Back

The growth factor is the base 'b' in the function f(x) = a(b)^x, which indicates how much the function increases for each unit increase in x.

Front

What is the decay factor in an exponential function?

Back

The decay factor is the base 'b' in the function f(x) = a(b)^x when 0 < b < 1, indicating a decrease in value as x increases.

Front

If f(x) = 3(2)^x, what is the initial value?

Back

The initial value is 3.

Front

If f(x) = 5(0.5)^x, what is the growth/decay factor?

Back

The decay factor is 0.5.

Front

What is the common ratio in the function f(x) = 2(4)^x?

Back

The common ratio is 4.

Front

In the function f(x) = 800(0.85)^x, what does 0.85 represent?

Back

0.85 represents the decay factor, indicating a decrease of 15% each time.

Front

How does the value of 'b' affect the graph of an exponential function?

Back

If b > 1, the graph shows exponential growth; if 0 < b < 1, the graph shows exponential decay.