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What is an exponential growth function?

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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.

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

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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.

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What is the formula for compound interest?

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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.

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

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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.

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

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y = 1400(1.09)^x.

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

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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.

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

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$2708.63.

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

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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.

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

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$2,225.54.

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

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