Exponential Review

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 a positive real number, and x is the exponent.

Front

What characterizes a linear function?

Back

A linear function is characterized by a constant rate of change, represented by the equation y = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.HSF-LE.A.1B

Front

How do you identify an exponential growth situation?

Back

Exponential growth occurs when a quantity increases by a fixed percentage over equal time intervals, often modeled by the equation y = a(1 + r)^t.

Tags

CCSS.HSF-LE.A.1A

Front

What is the difference between growth and decay in exponential functions?

Back

Growth occurs when the base of the exponential function is greater than 1 (e.g., y = a(2^x)), while decay occurs when the base is between 0 and 1 (e.g., y = a(0.5^x)).

Tags

CCSS.HSF-IF.C.8B

Front

What does the expression 70(2^5) represent?

Back

It represents the size of James' giant peach after 5 weeks, starting from an initial size of 70 inches and doubling in size each week.

Tags

CCSS.HSF.BF.A.2

Front

What is the general form of an exponential decay function?

Back

The general form is f(x) = a(b^x), where 0 < b < 1, indicating that the quantity decreases over time.

Front

How can you determine if a graph represents a linear or exponential function?

Back

A linear graph will show a straight line, while an exponential graph will show a curve that increases or decreases rapidly.

Tags

CCSS.8.F.A.3

Front

What does the term 'base' refer to in an exponential function?

Back

The base is the constant factor that is raised to the power of the variable in an exponential function, determining the rate of growth or decay.

Tags

CCSS.HSF-IF.C.8B

Front

What is the significance of the exponent in an exponential function?

Back

The exponent indicates how many times the base is multiplied by itself, affecting the growth rate of the function.

Tags

CCSS.HSF-IF.C.8B

Front

How do you write an expression for exponential growth?

Back

An expression for exponential growth can be written as y = a(1 + r)^t, where a is the initial amount, r is the growth rate, and t is time.

Tags

CCSS.HSF-IF.C.8B