Exponential Growth and Decay

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What is Exponential Growth?

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Exponential Growth occurs when a quantity increases by a consistent percentage over a period of time, resulting in a rapid increase. For example, if a population doubles every year, it is experiencing exponential growth.

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What is Exponential Decay?

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Exponential Decay occurs when a quantity decreases by a consistent percentage over a period of time. For example, if a radioactive substance loses half of its mass every year, it is experiencing exponential decay.

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What is the general formula for exponential growth?

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The general formula for exponential growth is y = a(1 + r)^x, where 'a' is the initial amount, 'r' is the growth rate, and 'x' is the time.

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What is the general formula for exponential decay?

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The general formula for exponential decay is y = a(1 - r)^x, where 'a' is the initial amount, 'r' is the decay rate, and 'x' is the time.

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In the equation y = 5000(1 - 0.30)^x, what does 5000 represent?

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In this equation, 5000 represents the initial quantity of bacteria.

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In the equation y = 5000(1 - 0.30)^x, what does 0.30 represent?

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In this equation, 0.30 represents the decay rate of the bacteria, indicating a 30% decrease each year.

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

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In exponential functions, 'x' typically represents time, measured in years or other time units.

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How do you determine if a function is exponential growth or decay?

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If the base of the exponent is greater than 1, it is exponential growth. If the base is between 0 and 1, it is exponential decay.

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What is the value of 'a' in the function f(x) = 300(1.16)^x?

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In the function f(x) = 300(1.16)^x, 'a' is 300, which is the starting term.

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How do you calculate the amount in a savings account with compound interest?

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To calculate the amount in a savings account with compound interest, use the formula A = P(1 + r/n)^(nt), where A is the amount, P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.