Q2W4 Flashcard 2 Exponents / Growth / Decay

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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 the base (a positive real number), and 'x' is the exponent. It shows rapid growth or decay.

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How do you convert a percentage to a decimal?

Back

To convert a percentage to a decimal, divide the percentage by 100. For example, 11.2% becomes 0.112.

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What is the formula for compound interest?

Back

The formula for compound interest is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, P is the principal amount, 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 does the term 'growth factor' mean in exponential functions?

Back

The growth factor is the base of the exponential function when it represents growth. For example, in the function y = a(1 + r)^x, the growth factor is (1 + r).

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What does the term 'decay factor' mean in exponential functions?

Back

The decay factor is the base of the exponential function when it represents decay. For example, in the function y = a(1 - r)^x, the decay factor is (1 - r).

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How do you find the x-intercept of a function?

Back

To find the x-intercept of a function, set y = 0 and solve for x.

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What is scientific notation?

Back

Scientific notation is a way of expressing numbers that are too large or too small in a compact form, typically in the format a x 10^n, where 1 ≤ a < 10 and n is an integer.

Front

How do you add numbers in scientific notation?

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To add numbers in scientific notation, first ensure they have the same exponent. If not, adjust one of the numbers. Then, add the coefficients and keep the common exponent.

Front

What is the initial amount in an exponential growth function?

Back

The initial amount in an exponential growth function is the value of the function when x = 0, represented by 'a' in the function y = a(1 + r)^x.

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What is the difference between growth and decay in exponential functions?

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Growth occurs when the base of the exponential function is greater than 1, while decay occurs when the base is between 0 and 1.