Exponential Functions

Front

What is an exponential function?

Back

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 base 'b' in an exponential function represent?

Back

The base 'b' determines the rate of growth or decay. If b > 1, the function represents exponential growth; if 0 < b < 1, it represents exponential decay.

Tags

CCSS.HSF-IF.C.8B

Front

What is the general form of an exponential growth function?

Back

f(x) = a(b^x) where b > 1.

Front

What is the general form of an exponential decay function?

Back

f(x) = a(b^x) where 0 < b < 1.

Front

In the function A = P(1 + r)^t, what does 'P' represent?

Back

'P' represents the principal amount or the initial investment.

Tags

CCSS.HSF.LE.B.5

Front

In the function A = P(1 + r)^t, what does 'r' represent?

Back

'r' represents the rate of interest (as a decimal) per time period.

Front

In the function A = P(1 + r)^t, what does 't' represent?

Back

't' represents the number of time periods the money is invested or borrowed.

Tags

CCSS.HSF.LE.B.5

Front

What is the y-intercept in an exponential function?

Back

The y-intercept is the value of the function when x = 0, which is equal to 'a' in the function f(x) = a(b^x).

Tags

CCSS.HSF-IF.C.7E

Front

How do you identify an exponential function from a table of values?

Back

An exponential function will show a constant ratio between consecutive outputs when the inputs are equally spaced.

Tags

CCSS.HSF-LE.A.1A

Front

What is the difference between linear and exponential growth?

Back

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