Front

What is an exponential function?

Back

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

Front

How do you identify the base in an exponential function?

Back

The base 'b' in an exponential function y = ab^x is the number that is raised to the power of 'x'. It determines the growth or decay rate of the function.

Tags

CCSS.HSF-IF.C.8B

Front

What does it mean for a function to triple every day?

Back

If a function triples every day, it means that the value of the function is multiplied by 3 for each unit increase in the independent variable (usually time). This can be represented as y = a(3^x), where 'a' is the initial amount.

Tags

CCSS.HSF-IF.C.8B

Front

How do you write an exponential function from a word problem?

Back

To write an exponential function from a word problem, identify the initial value and the growth/decay factor, then use the form y = a(b^x), where 'a' is the initial value and 'b' is the growth/decay factor.

Tags

CCSS.HSF.LE.A.2

Front

What is the general form of an exponential growth function?

Back

The general form of an exponential growth function is y = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

Front

What is the general form of an exponential decay function?

Back

The general form of an exponential decay function is y = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

Tags

CCSS.HSF-IF.C.8B

Front

How can you determine if a function is exponential from a table of values?

Back

A function is exponential if the ratio of consecutive outputs (y-values) is constant when the inputs (x-values) increase by the same amount.

Tags

CCSS.HSF-LE.A.1A

Front

What is the significance of the initial value 'a' in an exponential function?

Back

The initial value 'a' represents the starting amount or value of the function when x = 0.

Tags

CCSS.HSF.LE.B.5

Front

How do you graph an exponential function?

Back

To graph an exponential function, plot the initial value at x = 0, then use the base to determine the growth or decay for other values of x, creating a smooth curve.

Tags

CCSS.HSF-IF.C.7E

Front

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

Back

Changing the base 'b' affects the rate of growth or decay; a base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

Tags

CCSS.HSF-IF.C.7E