Exponential Growth and Decay

Front

What is exponential growth?

Back

Exponential growth occurs when the increase of a quantity is proportional to its current value, leading to growth at an increasing rate over time.

Tags

CCSS.HSF-LE.A.1A

Front

What is exponential decay?

Back

Exponential decay is the decrease of a quantity at a rate proportional to its current value, resulting in a rapid decline that slows over time.

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 = 15(1.35)^x, what does the number 15 represent?

Back

The number 15 represents the initial amount before any growth occurs.

Tags

CCSS.HSF.LE.B.5

Front

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

Back

The value 0.015 represents the decay rate of 1.5% per year.

Tags

CCSS.HSF-IF.C.8B

Front

How do you convert a percentage growth rate to a decimal for use in exponential functions?

Back

To convert a percentage growth rate to a decimal, divide the percentage by 100. For example, 35% becomes 0.35.

Tags

CCSS.HSF-IF.C.8B

Front

What does the exponent in an exponential function represent?

Back

The exponent represents the number of time periods (years, months, etc.) that have passed.

Tags

CCSS.HSF-IF.C.8B

Front

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

Back

The base indicates the growth or decay factor; a base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

Tags

CCSS.HSF-IF.C.8B

Front

If a population of 1500 deer decreases by 1.5% per year, what will be the population after 10 years?

Back

Using the function y = 1500(1 - 0.015)^10, the population will be approximately 1290 deer.

Tags

CCSS.HSF-LE.A.1C