Exponential Growth and Decay

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What is Exponential Growth?

Back

Exponential Growth occurs when a quantity increases by a fixed percentage over a period of time, resulting in a rapid increase. Example: A population that grows by 10% each year.

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What is Exponential Decay?

Back

Exponential Decay occurs when a quantity decreases by a fixed percentage over a period of time, leading to a rapid decrease. Example: A radioactive substance that decays by 5% each year.

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What is the formula for Exponential Growth?

Back

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

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What is the formula for Exponential Decay?

Back

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

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What does the variable 'a' represent in exponential functions?

Back

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

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How do you determine the initial value in the function f(x) = 300(1.16)^x?

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The initial value is the coefficient of the function when x=0, which is 300.

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If a population of fish decreases by 6% per year, what is the decay factor?

Back

The decay factor is 1 - 0.06 = 0.94.

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

Back

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

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What is the value of a home worth today if it was purchased for $160,000 and appreciates at 5% per year for 20 years?

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The value today is approximately $424,527.63.

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Classify the model A=1200(0.85)^6 as Exponential Growth or Decay.

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This model is classified as Exponential Decay.