exponential growth and decay

Front

What is exponential growth?

Back

Exponential growth occurs when a quantity increases by a consistent percentage over a period of time, resulting in a rapid increase as time goes on.

Front

What is exponential decay?

Back

Exponential decay occurs when a quantity decreases by a consistent percentage over a period of time, leading to a rapid decrease as time progresses.

Front

What is the formula for exponential growth?

Back

The formula is y = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

Front

What is the formula for exponential decay?

Back

The formula is 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 100 increases by 20% each year, what will it be after 1 year?

Back

120 (100 * 1.20 = 120).

Front

If a population of 200 decreases by 10% each year, what will it be after 1 year?

Back

180 (200 * 0.90 = 180).

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 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.

Front

How do you calculate the future value of an investment using exponential growth?

Back

Use the formula: Future Value = Present Value * (1 + r)^t.