Exponential Modeling

Front

What is an exponential growth function?

Back

An exponential growth function is a mathematical expression that describes a quantity increasing at a constant percentage rate over time, typically represented as y = a(1 + r)^x, where 'a' is the initial amount, 'r' is the growth rate, and 'x' is time.

Front

How do you write an exponential growth function for a value that increases by a certain percentage each year?

Back

To write an exponential growth function for a value that increases by a certain percentage each year, use the formula y = a(1 + r)^x, where 'a' is the initial value, 'r' is the growth rate (as a decimal), and 'x' is the number of years.

Front

What is the formula for compound interest?

Back

The formula for compound interest is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, P is the principal amount (the initial amount of money), r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the number of years.

Front

What does 'compounded continuously' mean in terms of interest?

Back

Compounded continuously means that interest is calculated and added to the principal at every possible moment, leading to the formula A = Pe^(rt), where e is the base of the natural logarithm, P is the principal, r is the interest rate, and t is time.

Front

If a painting's value is $1400 and increases by 9% each year, what is the exponential growth function?

Back

y = 1400(1.09)^x.

Front

How do you calculate the future value of an investment with daily compounding interest?

Back

To calculate the future value of an investment with daily compounding interest, use the formula A = P(1 + r/365)^(365t), where P is the principal, r is the annual interest rate, and t is the number of years.

Front

What is the future value of $2,200 invested at 5.2% interest compounded daily for 4 years?

Back

$2708.63.

Front

What is the formula for calculating the balance of an account with quarterly compounding interest?

Back

The formula is A = P(1 + r/4)^(4t), where P is the principal, r is the annual interest rate, and t is the number of years.

Front

If $1,000 is invested at 16% interest compounded continuously for 5 years, what is the ending balance?

Back

$2,225.54.

Front

What is the attendance growth model for a museum with an initial attendance of 250 people increasing at 3% per month?

Back

y = 250(1.03)^x, where x is the number of months.