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 grows by 10% each year, it will grow faster each subsequent year.

Front

What is Exponential Decay?

Back

Exponential Decay occurs when a quantity decreases by a consistent percentage over time, leading to a rapid decrease. For example, radioactive substances decay at a constant rate.

Front

What is the formula for Exponential Growth?

Back

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

Front

What does the 'a' represent in the exponential function?

Back

The 'a' represents the initial value or starting amount before any growth or decay occurs.

Front

If a population of 100 increases by 20% each year, what will it be after 3 years?

Back

The population will be approximately 182.43 after 3 years.

Front

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

Back

If the growth rate (r) is positive, it represents growth. If the decay rate (r) is negative, it represents decay.

Front

What is the initial value for the function: f(x) = 200(1.05)^x?

Back

The initial value is 200.

Front

If a car's value decreases by 15% each year, what is the decay factor?

Back

The decay factor is 0.85 (1 - 0.15).

Front

What is the value of an investment of $1,000 that grows at a rate of 8% per year after 5 years?

Back

The value will be approximately $1,469.33 after 5 years.