NC Math 3 Check-Up 1

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How do you calculate the future population given an initial population and a growth rate?

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Use the formula: Future Population = Initial Population * (1 + growth rate)^(number of years).

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What is the inverse of a function?

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The inverse of a function f(x) is a function that reverses the effect of f. If f(a) = b, then f^(-1)(b) = a.

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Which type of function has an inverse that is also a function?

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A function is invertible if it is one-to-one (each output is produced by exactly one input).

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How do you find the inverse of a function graphically?

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The graph of the inverse function is a reflection of the original function across the line y = x.

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What is the formula for exponential growth?

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The formula is P(t) = P_0 * e^(rt), where P_0 is the initial amount, r is the growth rate, and t is time.

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What does it mean for a function to be one-to-one?

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A function is one-to-one if it never takes the same value twice; that is, f(a) = f(b) implies a = b.

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What is the relationship between logarithms and exponents?

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How do you determine if a function has an inverse?

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A function has an inverse if it is one-to-one and passes the horizontal line test.