Exponential Growth and Decay

Front

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

Back

0.8

Front

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

Back

1.8

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.

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.

Front

What does the term 'exponential growth' mean?

Back

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

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.

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.

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.

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.

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.