Exponential Growth and Decay Flashcard

Front

What is the formula for exponential growth?

Back

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

Front

Define half-life in the context of decay.

Back

Half-life is the time required for a quantity to reduce to half its initial amount.

Front

What does a 6% annual decrease mean in terms of exponential decay?

Back

It means that each year, the population is multiplied by (1 - 0.06) or 0.94.

Front

How do you calculate the remaining amount after a certain number of years using the decay formula?

Back

Use the formula y = a(1 - r)^t, substituting 'a' for the initial amount, 'r' for the decay rate, and 't' for the number of years.

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

If a population grows at a rate of 2.2%, what is the growth factor?

Back

The growth factor is 1 + 0.022 = 1.022.

Front

How do you find the value of an investment after a certain number of years with compound interest?

Back

Use the formula A = P(1 + r/n)^(nt), where 'P' is the principal, 'r' is the annual interest rate, 'n' is the number of times interest is compounded per year, and 't' is the number of years.

Front

What is depreciation in financial terms?

Back

Depreciation is the reduction in the value of an asset over time, often due to wear and tear.

Front

How do you calculate the value of an asset after depreciation?

Back

Use the formula V = P(1 - r)^t, where 'P' is the initial value, 'r' is the depreciation rate, and 't' is the number of years.