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 time progresses.

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 time progresses.

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.

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.

Front

If a population of 1000 increases by 20% each year, what will be the population after 1 year?

Back

1200

Front

If a car worth $20,000 depreciates at a rate of 10% per year, what will it be worth after 1 year?

Back

$18,000

Front

What does the term 'initial amount' refer to in exponential functions?

Back

The initial amount is the starting value of the quantity before any growth or decay occurs.

Front

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

Back

Divide the percentage by 100. For example, 35% becomes 0.35.

Front

What is the effect of a higher growth rate on the outcome of an exponential growth function?

Back

A higher growth rate results in a faster increase in the quantity over time.

Front

What is the effect of a higher decay rate on the outcome of an exponential decay function?

Back

A higher decay rate results in a faster decrease in the quantity over time.