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.

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.

Front

How do you express exponential growth mathematically?

Back

Exponential growth can be expressed as y = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

Front

How do you express exponential decay mathematically?

Back

Exponential decay can be expressed as y = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

Front

What is the decay factor in exponential decay?

Back

The decay factor is calculated as (1 - r), where 'r' is the decay rate.

Front

What is the growth factor in exponential growth?

Back

The growth factor is calculated as (1 + r), where 'r' is the growth rate.

Front

If a population of 10,000 decreases by 5% per year, what is the population after one year?

Back

The population after one year is 10,000(1 - 0.05) = 9,500.

Front

How do you determine the size of an object that doubles in size every week after 'n' weeks?

Back

The size can be determined using the expression: initial size * (2^n).

Front

What is the formula to calculate the future value of an investment with exponential growth?

Back

The future value can be calculated using the formula: FV = P(1 + r)^t, where P is the principal amount, r is the rate of return, and t is the time in years.

Front

What is the formula to calculate the future value of an investment with exponential decay?

Back

The future value can be calculated using the formula: FV = P(1 - r)^t, where P is the principal amount, r is the decay rate, and t is the time in years.