Writing Exponential Functions from Word Problems

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 initial value (y-intercept) represent in an exponential function?

Back

The initial value (or y-intercept) represents the value of the function when x = 0. It indicates the starting amount before any growth or decay occurs.

Tags

CCSS.HSF.LE.B.5

Front

How do you identify exponential growth in a function?

Back

Exponential growth occurs when the base 'b' in the function f(x) = a(b)^x is greater than 1.

Tags

CCSS.HSF-IF.C.8B

Front

How do you identify exponential decay in a function?

Back

Exponential decay occurs when the base 'b' in the function f(x) = a(b)^x is between 0 and 1.

Tags

CCSS.HSF-IF.C.8B

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is f(t) = 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

Front

What is the formula for exponential decay?

Back

The formula for exponential decay is f(t) = 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 do you write an exponential function from a word problem?

Back

Identify the initial value, the rate of growth or decay, and the time variable. Use the formula f(t) = a(1 ± r)^t to write the function.

Tags

CCSS.HSF.LE.A.2

Front

What does the term 'rate of increase' mean in the context of exponential functions?

Back

The rate of increase refers to the percentage by which the initial value grows over a specific period of time.

Tags

CCSS.HSF-IF.C.8B

Front

What does the term 'rate of decrease' mean in the context of exponential functions?

Back

The rate of decrease refers to the percentage by which the initial value declines over a specific period of time.

Tags

CCSS.HSF-IF.C.8B

Front

If a function is modeled by f(x) = 500(0.8)^x, what does 0.8 represent?

Back

In this function, 0.8 represents the decay factor, indicating that the quantity decreases by 20% each time period.

Tags

CCSS.HSF.LE.B.5