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 decrease in a quantity at a rate proportional to its current value, resulting in a rapid decline that slows over time.

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

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

Back

Use the formula P = P0(1 - r)^t, where P0 is the initial population, r is the decay rate, and t is 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 A is the amount of money accumulated after n years, P is the principal amount, r is the annual interest rate, and t is the number of years.

Front

What does the variable 'b' represent in the function f(x) = a(b)^x?

Back

In this function, 'b' is the base or common ratio that indicates the growth (b > 1) or decay (0 < b < 1) factor.

Front

If a population of 10,000 decreases by 10% each year, what is the population after 1 year?

Back

The population after 1 year is 10,000(1 - 0.10) = 9,000.

Front

What is the value of a printer worth after 5 years if it depreciates at 20% per year?

Back

The value after 5 years is V = 35,000(1 - 0.20)^5 = $14,696.83.

Front

What is the significance of the initial value 'a' in exponential functions?

Back

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