Exponential Modeling

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What is exponential growth?

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Exponential growth occurs when a quantity increases by a constant percentage over a period of time, resulting in a rapid increase. The general formula is: 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 exponential decay?

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Exponential decay occurs when a quantity decreases by a constant percentage over time. The general formula is: 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 future value of an investment compounded continuously?

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The formula for continuous compounding is: A = Pe^(rt), 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, and 't' is the time in years.

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What is the formula for exponential growth?

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The formula for exponential growth is: 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 the formula for exponential decay?

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

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If a population of 4,000 mosquitoes grows at a rate of 25% per month, how many will there be after 4 months?

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After 4 months, the population will be approximately 9766 mosquitoes.

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What does the base of an exponential function indicate?

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The base of an exponential function indicates the growth or decay factor. If the base is greater than 1, it represents growth; if the base is between 0 and 1, it represents decay.

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How can you determine if a function represents exponential growth or decay?

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To determine if a function represents exponential growth or decay, check the base of the exponential term. If the base is greater than 1, it indicates growth; if the base is less than 1, it indicates decay.

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What is the initial amount in the function y = 15(1.35)^x?

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The initial amount in the function y = 15(1.35)^x is 15.

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What is the growth rate in the function y = 15(1.35)^x?

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The growth rate in the function y = 15(1.35)^x is 35%.