Exponential Growth and Decay Applications

Front

What is the general formula for exponential growth?

Back

The general formula for exponential growth is y = y_0 e^{rt}, where y is the final amount, y_0 is the initial amount, r is the growth rate, and t is time.

Tags

CCSS.HSF-LE.A.1A

Front

What is the general formula for exponential decay?

Back

The general formula for exponential decay is y = y_0 e^{-rt}, where y is the final amount, y_0 is the initial amount, r is the decay rate, and t is time.

Tags

CCSS.HSF-LE.A.1A

Front

What does the variable 'n' represent in compound interest formulas?

Back

In compound interest formulas, 'n' represents the number of times interest is compounded per year.

Front

What is the formula for calculating the future value of an investment compounded quarterly?

Back

The formula is y = y_0(1 + r/n)^{nt}, where y_0 is the initial investment, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.

Front

What is half-life in the context of exponential decay?

Back

Half-life is the time required for a quantity to reduce to half its initial value.

Front

How do you calculate the remaining amount of a substance after a certain time using half-life?

Back

You can use the formula y = y_0(1/2)^{(t/H)}, where y_0 is the initial amount, t is the elapsed time, and H is the half-life.

Front

What is the difference between continuous compounding and discrete compounding?

Back

Continuous compounding calculates interest at every possible instant, while discrete compounding calculates interest at specific intervals (e.g., annually, quarterly).

Front

What is the formula for continuous compounding?

Back

The formula for continuous compounding is y = y_0 e^{rt}, where y_0 is the initial amount, r is the interest rate, and t is time.

Front

How do you determine the time required for an investment to double using the rule of 72?

Back

The rule of 72 states that you can estimate the time to double an investment by dividing 72 by the annual interest rate (in percentage).

Tags

CCSS.HSF.IF.A.2

Front

What is the significance of the base 'e' in exponential functions?

Back

The base 'e' (approximately 2.718) is a mathematical constant that is the limit of (1 + 1/n)^n as n approaches infinity, and it is used in continuous growth and decay models.

Tags

CCSS.HSF-IF.C.8B