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.

Tags

CCSS.HSF.LE.B.5

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.

Tags

CCSS.HSF-IF.C.7E

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.

Tags

CCSS.HSF-IF.C.8B

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.

Tags

CCSS.HSF-IF.C.8B

Front

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

Back

The initial value is 3.

Tags

CCSS.HSF.LE.B.5

Front

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

Back

The decay factor is 0.5.

Tags

CCSS.HSF-IF.C.8B

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.

Tags

CCSS.HSF.LE.B.5

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.

Tags

CCSS.HSF-IF.C.7E