Exponential Growth Decay in real life(24-25)

Front

What is Exponential Growth?

Back

Exponential Growth occurs when a quantity increases by a fixed percentage over a period of time, leading to rapid increases as the base amount grows.

Front

What is Exponential Decay?

Back

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

Front

What is 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 time.

Front

What is 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 time.

Front

If a population of 4,000 mosquitoes grows at 25% per month, how many will there be after 4 months?

Back

9765 mosquitoes.

Front

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

Back

Use the formula A = P(1 + r)^t, substituting P for the initial investment, r for the interest rate, and t for 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 does a decay rate of 5% mean for an asset's value?

Back

It means that each year, the asset's value will decrease to 95% of its value from the previous year.

Front

How do you determine if a model represents growth or decay?

Back

If the model has a base greater than 1, it represents growth; if the base is less than 1, it represents decay.

Front

What is the value of a $35,000 printer after 8 years with a 5% annual depreciation?

Back

$23,219.72.