Exponential Growth and Decay

Front

What is exponential growth?

Back

Exponential growth occurs when a quantity increases by a fixed percentage over a period of time, resulting in a rapid increase as the base amount grows.

Tags

CCSS.HSF-LE.A.1A

Front

What is exponential decay?

Back

Exponential decay occurs when a quantity decreases by a fixed percentage over a period of time, leading to a rapid decrease as the base amount shrinks.

Tags

CCSS.HSF-IF.C.8B

Front

What is the general formula for exponential growth?

Back

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

Front

What is the general formula for exponential decay?

Back

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

In the function y = 1500(1 - 0.015)^t, what does 1500 represent?

Back

The initial population of deer.

Tags

CCSS.HSF.LE.B.5

Front

In the function f(x) = 417(1.0375)^x, what does 1.0375 represent?

Back

The growth factor, which includes the initial amount plus the growth rate (3.75%).

Tags

CCSS.HSF.LE.B.5

Front

What does the term 'decay rate' mean?

Back

The decay rate is the percentage by which a quantity decreases over a specific period of time.

Tags

CCSS.HSF-IF.C.8B

Front

How do you convert a percentage to a decimal for calculations?

Back

To convert a percentage to a decimal, divide the percentage by 100.

Front

What is the significance of the initial value in exponential functions?

Back

The initial value represents the starting amount before any growth or decay occurs.

Tags

CCSS.HSF-IF.C.8B

Front

What does the graph of an exponential growth function look like?

Back

The graph rises sharply and becomes steeper over time, indicating rapid growth.

Tags

CCSS.HSF-IF.C.7E