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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, represented by the equation A = P(1 + r)^t, where A is the amount, P 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 consistent percentage over time, represented by the equation A = P(1 - r)^t, where A is the amount, P is the initial amount, r is the decay rate, and t is time.

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How can you identify Exponential Growth from an equation?

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An equation represents Exponential Growth if the base of the exponent is greater than 1, e.g., A = 10(1.01)^t.

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How can you identify Exponential Decay from an equation?

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An equation represents Exponential Decay if the base of the exponent is between 0 and 1, e.g., A = 10(0.99)^t.

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What does the correlation coefficient (r) indicate?

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The correlation coefficient (r) indicates the strength and direction of a linear relationship between two variables, ranging from -1 (perfect negative correlation) to +1 (perfect positive correlation).

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What is the initial value in an exponential function?

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The initial value in an exponential function is the value of the function when time (t) is zero, represented by P in the equation A = P(1 + r)^t.

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What is the difference between Linear Growth and Exponential Growth?

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Linear Growth increases by a constant amount over equal intervals, while Exponential Growth increases by a percentage of the current value, leading to faster growth over time.

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What is an example of Exponential Growth?

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An example of Exponential Growth is population growth, where the population increases by a percentage each year.

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What is an example of Exponential Decay?

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An example of Exponential Decay is radioactive decay, where the quantity of a radioactive substance decreases by a percentage over time.

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What does it mean if r = 0 in a correlation?

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If r = 0, it means there is no correlation between the two variables; they do not have a linear relationship.