Writing Exponential Growth and Decay Models

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What is an exponential growth model?

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An exponential growth model describes a situation where a quantity increases at a rate proportional to its current value, often represented by the equation y = 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 an exponential decay model?

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An exponential decay model describes a situation where a quantity decreases at a rate proportional to its current value, often represented by the equation y = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

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How do you calculate the decay factor for depreciation?

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The decay factor can be calculated as 1 - (decay rate). For example, if an item depreciates at 8%, the decay factor is 1 - 0.08 = 0.92.

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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, 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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Convert 11.2% to a decimal.

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0.112

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If a printer costs $35,000 and depreciates at 5% per year, what will its value be after 8 years?

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$23,219.72

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A fish population starts at 8,000 and decreases by 6% per year. What will the population be after 10 years?

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4,309

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What is the initial value in an exponential model?

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The initial value is the starting amount before any growth or decay occurs, often represented by 'a' in the equations.

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What does the term 'compounded annually' mean?

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Compounded annually means that the interest is calculated and added to the principal once per year.

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How do you find the value of an investment after a certain number of years with compound interest?

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You can find the value by using the compound interest formula A = P(1 + r/n)^(nt) and substituting the appropriate values for P, r, n, and t.