Write and Evaluate Exponential 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.

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How do you identify a linear function?

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A linear function can be identified by its constant rate of change, represented by the equation f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What is the half-life of a substance?

Back

The half-life is the time required for a quantity to reduce to half its initial amount. It is commonly used in radioactive decay and pharmacology.

Front

Write the exponential decay function for a substance with a half-life of 6 hours starting with 100 mg.

Back

f(x) = 100 * (1/2)^(x/6), where x is the time in hours.

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What does the term 'exponential growth' mean?

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Exponential growth refers to an increase that occurs at a rate proportional to the current value, often modeled by f(t) = a * e^(kt), where k is a positive constant.

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How do you calculate the future value of an investment with exponential growth?

Back

Use the formula f(t) = P(1 + r)^t, where P is the principal amount, r is the growth rate, and t is the time in years.

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What is the difference between linear and exponential growth?

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

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How do you evaluate an exponential function at a specific point?

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Substitute the value of x into the function and calculate the result. For example, for f(x) = 2^x, to find f(3), calculate 2^3 = 8.

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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.

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How can you determine if a function is exponential from a table of values?

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If the ratio of consecutive outputs is constant, the function is exponential. For example, if f(1)/f(0) = f(2)/f(1), it indicates exponential behavior.