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. Example: A population that doubles every year.

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, leading to a rapid decline. Example: Radioactive substances losing half their mass over time.

Tags

CCSS.HSF-IF.C.8B

Front

What is the general formula for exponential growth?

Back

The general formula is 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

The general formula 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

What does the 'a' represent in the exponential function?

Back

In the function y = a(1 + r)^t, 'a' represents the initial amount or starting value before growth or decay.

Tags

CCSS.HSF.LE.B.5

Front

What does the 'r' represent in the exponential function?

Back

In the function y = a(1 + r)^t, 'r' represents the rate of growth (if positive) or decay (if negative) expressed as a decimal.

Tags

CCSS.HSF-IF.C.8B

Front

How do you find the half-life of a substance?

Back

The half-life is the time required for a quantity to reduce to half its initial value. It can be calculated using the formula: Half-life = ln(2) / decay rate.

Front

What is a multiplier in exponential decay?

Back

The multiplier (b-value) in exponential decay is calculated as (1 - decay rate). For example, if the decay rate is 29%, the multiplier is 0.71.

Tags

CCSS.HSF-IF.C.8B

Front

How do you convert a percentage decrease to a multiplier?

Back

To convert a percentage decrease to a multiplier, subtract the percentage (as a decimal) from 1. For example, a 20% decrease is represented as 1 - 0.20 = 0.80.

Tags

CCSS.7.EE.A.1

Front

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

Back

The base in an exponential function 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