Key Characteristics on Exponentials Functions

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a * b^x, where 'a' is a constant, 'b' is a positive real number, and 'x' is the exponent.

Front

What is the base of an exponential function?

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The base of an exponential function is the constant 'b' in the function f(x) = a * b^x, which determines the rate of growth or decay.

Front

What is exponential growth?

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Exponential growth occurs when a quantity increases by a fixed percentage over a period of time, resulting in a rapid increase.

Front

What is exponential decay?

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Exponential decay occurs when a quantity decreases by a fixed percentage over a period of time, leading to a rapid decrease.

Front

What is the horizontal asymptote of an exponential function?

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The horizontal asymptote of an exponential function is the line that the graph approaches as x approaches infinity or negative infinity; for most exponential functions, this is y = 0.

Front

What is the y-intercept of the function y = 2^x?

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The y-intercept of the function y = 2^x is (0, 1), since 2^0 = 1.

Front

What happens to f(x) as x approaches infinity in an exponential growth function?

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As x approaches infinity in an exponential growth function, f(x) approaches infinity.

Front

What is the x-intercept of an exponential function?

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An exponential function does not have an x-intercept; it never crosses the x-axis.

Front

How do you calculate compound interest?

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Compound interest can be calculated using 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.

Front

What is the formula for continuous compound interest?

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The formula for continuous compound interest is A = Pe^(rt), where A is the amount, P is the principal, r is the annual interest rate, and t is the time in years.