Exponential Word Problems

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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 f(t) = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

Tags

CCSS.HSF-IF.C.8B

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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 investment), 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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How do you calculate the future value of an investment?

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To calculate the future value of an investment, use the formula FV = PV(1 + r)^n, where FV is the future value, PV is the present value (initial investment), r is the annual interest rate (as a decimal), and n is the number of years.

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CCSS.HSF.BF.A.2

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What does it mean for a population to decrease by a certain percentage each year?

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A population decreasing by a certain percentage each year means that the population reduces by that percentage of its current size annually, which can be modeled using an exponential decay function.

Tags

CCSS.HSF-LE.A.1A

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What is the difference between exponential growth and exponential decay?

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Exponential growth occurs when a quantity increases by a constant percentage over time, while exponential decay occurs when a quantity decreases by a constant percentage over time.

Tags

CCSS.HSF-IF.C.8B

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If an investment of $1,000 grows to $1,500 in 5 years, what is the annual growth rate?

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To find the annual growth rate, use the formula r = (FV/PV)^(1/n) - 1. Here, FV = 1500, PV = 1000, and n = 5. The growth rate is approximately 8.45%.

Tags

CCSS.HSF.LE.A.4

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What is the formula for exponential decay?

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The formula for exponential decay is f(t) = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

Tags

CCSS.HSF-IF.C.8B

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How do you model a situation where a quantity increases by a percentage each year?

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You can model this situation using the exponential growth function f(t) = a(1 + r)^t, where 'a' is the initial quantity, 'r' is the growth rate, and 't' is the number of years.

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What is the significance of the base in an exponential function?

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The base in an exponential function determines the rate of growth or decay. A base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

Tags

CCSS.HSF-IF.C.8B

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How do you determine the time it takes for an investment to double?

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To determine the time it takes for an investment to double, use the Rule of 72: divide 72 by the annual interest rate (as a percentage). For example, at a 6% interest rate, it takes approximately 12 years to double.

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CCSS.HSF.LE.A.4