Exponential Growth and Decay

Front

What is the decay factor if the decay rate is 20%?

Back

0.8

Tags

CCSS.HSF-IF.C.8B

Front

What is the growth factor if the growth rate is 80%?

Back

1.8

Tags

CCSS.HSF-IF.C.8B

Front

What is the general form of the equation for exponential decay?

Back

y = a(1 - r)^x, where a is the initial amount, r is the decay rate, and x is time.

Tags

CCSS.HSF-IF.C.8B

Front

How can you identify an exponential decay model from an equation?

Back

If the base of the exponent is less than 1, it represents exponential decay.

Tags

CCSS.HSF-IF.C.8B

Front

What does the term 'exponential growth' mean?

Back

Exponential growth occurs when a quantity increases by a constant percentage over equal time intervals.

Tags

CCSS.HSF-IF.C.8B

Front

What is the formula for exponential growth?

Back

y = a(1 + r)^x, where a is the initial amount, r is the growth rate, and x is time.

Tags

CCSS.HSF-IF.C.8B

Front

If a quantity decreases by 20% each hour, what is the remaining amount after 3 hours if the initial amount is 100?

Back

y = 100(0.8)^3 = 51.2.

Tags

CCSS.HSF-LE.A.1C

Front

What is the difference between growth rate and decay rate?

Back

Growth rate refers to the percentage increase, while decay rate refers to the percentage decrease of a quantity.

Tags

CCSS.HSF-IF.C.8B

Front

How do you convert a percentage decay rate to a decay factor?

Back

Subtract the decay rate from 1. For a 20% decay rate, the decay factor is 1 - 0.20 = 0.80.

Tags

CCSS.HSF-IF.C.8B

Front

What does it mean if a model is classified as exponential decay?

Back

It means that the quantity decreases over time at a rate proportional to its current value.

Tags

CCSS.HSF-IF.C.8B