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. For example, if a population doubles every year, it is experiencing exponential growth.

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. For example, if a population decreases by 10% each year, it is experiencing exponential decay.

Front

How do you identify exponential growth or decay from a function?

Back

If the base of the exponential function is greater than 1, it represents growth. If the base is between 0 and 1, it represents decay.

Front

What is the formula for exponential growth?

Back

The formula for exponential growth 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 for exponential decay 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

What does the y-intercept represent in an exponential function?

Back

The y-intercept represents the initial value of the function when time (t) is zero.

Front

If a population of 1,000 decreases by 5% per year, what will the population be after 1 year?

Back

Population after 1 year = 1000(1 - 0.05) = 950.

Front

What is the effect of a higher decay rate on the amount over time?

Back

A higher decay rate results in a faster decrease in the amount over time.

Front

What is a real-world example of exponential growth?

Back

A common example of exponential growth is the spread of a virus, where each infected person can infect multiple others.

Front

What is a real-world example of exponential decay?

Back

A common example of exponential decay is radioactive decay, where unstable atoms lose energy over time.