7.6 Exponential Growth and Decay

Front

What is exponential growth?

Back

Exponential growth occurs when the increase in a quantity is proportional to its current value, leading to growth at an increasing rate over time.

Front

What is exponential decay?

Back

Exponential decay is the process of reducing an amount by a consistent percentage rate over a period of time, leading to a decrease that slows down as the quantity decreases.

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 the 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 the time.

Front

How do you calculate the population after a certain number of years with exponential decay?

Back

Use the formula A = P(1 - r)^t, substituting P for the initial population, r for the decay rate, and t for the number of years.

Front

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

Back

Use the formula A = P(1 + r)^t, where P is the initial investment, r is the annual growth rate, and t is the number of years.

Front

What does a decay rate of 50% mean?

Back

A decay rate of 50% means that the quantity decreases to half of its previous value each year.

Front

If a population of 4,000 mosquitoes grows at 25% per month, how do you find the population after 4 months?

Back

Use the formula A = P(1 + r)^t, where P = 4000, r = 0.25, and t = 4.

Front

What is the significance of the initial amount in exponential functions?

Back

The initial amount is the starting value from which growth or decay occurs, influencing the final outcome significantly.

Front

How do you interpret the growth factor in exponential growth?

Back

The growth factor (1 + r) indicates how much the quantity increases each period; for example, a growth factor of 1.35 means a 35% increase.