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, leading to rapid increases as the quantity grows.

Front

What is Exponential Decay?

Back

Exponential Decay occurs when a quantity decreases by a consistent percentage over a period of time, leading to rapid decreases as the quantity shrinks.

Front

Define the formula for Exponential Growth.

Back

The formula is A = P(1 + r)^t, where A is the amount after time t, P is the initial amount, r is the growth rate, and t is the time.

Front

Define the formula for Exponential Decay.

Back

The formula is A = P(1 - r)^t, where A is the amount after time t, P is the initial amount, r is the decay rate, and t is the time.

Front

What is the growth rate in the mosquito population problem?

Back

The growth rate is 25% per month.

Front

How do you calculate the future value of an investment with compound interest?

Back

Use the formula A = P(1 + r/n)^(nt), where A is the amount, 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 does depreciation mean in the context of assets?

Back

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

Front

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

Back

Use the formula A = P(1 - r)^t, where A is the value after t years, P is the initial value, r is the depreciation rate, and t is the number of years.

Front

What is the significance of the base in exponential functions?

Back

The base determines the rate of growth or decay; a base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

Front

What is the initial population of mosquitoes in the problem?

Back

The initial population is 4,000 mosquitoes.