Everything EXPONENTIALS

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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.

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What is the general form of an increasing exponential function?

Back

The general form of an increasing exponential function is f(x) = a * b^x, where 'a' > 0 and 'b' > 1.

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What is the asymptote of the exponential function y = b^x?

Back

The asymptote of the exponential function y = b^x is the line y = 0 (the x-axis).

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How do you determine the y-intercept of an exponential function?

Back

The y-intercept of an exponential function f(x) = a * b^x is found by evaluating f(0), which equals 'a'.

Front

What does it mean for a function to decrease exponentially?

Back

A function decreases exponentially if it can be modeled by f(x) = a * (1 - r)^x, where '0 < r < 1' and 'a' is the initial value.

Front

What is the value of the function f(x) = 40(0.95)^x when x = 1?

Back

f(1) = 40(0.95)^1 = 40 * 0.95 = 38.

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What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when a quantity increases by a constant percentage over time, while exponential decay occurs when a quantity decreases by a constant percentage over time.

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What is the base of an exponential function?

Back

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.

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How can you identify an exponential function from a set of data points?

Back

An exponential function can be identified if the ratio of consecutive y-values remains constant or if the logarithm of the y-values forms a linear relationship.

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What is the formula for exponential decay?

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The formula for exponential decay is f(t) = a * e^(-kt), where 'a' is the initial amount, 'k' is the decay constant, and 't' is time.