Exponential Functions Free Online FlashCards

What happens to exponents when like bases are multiplied?

Multiplication adds exponents: a^m a^n = a^(m+n).

What does a rational exponent represent?

A rational exponent represents a root: a^(1/n) = ⁿ√a, and a^(m/n) = ⁿ√(a^m).

What is the general form of an exponential function?

An exponential function has the form f(x) = ab^x, where a ≠ 0, b > 0, and b ≠ 1.

What are the domain and range of f(x) = ab^x when a > 0?

For f(x) = ab^x, the domain is all real numbers. If a > 0, the range is (0, ∞).

How does the base determine exponential growth or decay?

If b > 1, the function increases and models growth; if 0 < b < 1, it decreases and models decay.

What growth factor represents a percentage increase r?

A percentage increase of r uses the factor 1 + r. For a 7% increase, the factor is 1.07.

What decay factor represents a percentage decrease r?

A percentage decrease of r uses the factor 1 − r. For a 12% decrease, the factor is 0.88.

What model describes continuous growth or decay?

Continuous growth or decay is modeled by A(t) = A₀e^(kt). Positive k indicates growth; negative k indicates decay.

What formula models interest compounded n times per year?

Compound interest is modeled by A = P(1 + r/n)^(nt), where r is the decimal annual rate and n is the number of periods per year.

How can you distinguish exponential data from linear data?

Exponential data have approximately constant ratios for equal input increases, whereas linear data have constant differences.

How do you find b in y = ab^x from two points?

For two points, b = (y₂/y₁)^(1/(x₂−x₁)); then substitute b into either point to find a.

What is the horizontal asymptote of g(x) = Ab^(B(x−h)) + k?

In g(x) = Ab^(B(x−h)) + k, the horizontal asymptote is y = k.