Evaluating 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 the base (a positive real number), and 'x' is the exponent.

Front

What is the common ratio in an exponential function?

Back

The common ratio (or multiplier) in an exponential function is the base 'b' raised to the power of 'x'. It represents how much the function value changes as 'x' increases by 1.

Front

Evaluate the function f(x) = 2(4)^x for x = 1.

Back

f(1) = 2(4)^1 = 2 * 4 = 8.

Front

How do you find the value of an exponential function at a negative exponent?

Back

To find the value of an exponential function at a negative exponent, use the property b^(-n) = 1/(b^n). For example, w(-2) = 8^(-2) = 1/(8^2) = 1/64.

Front

What is the value of p(-3) if p(x) = 3^x?

Back

p(-3) = 3^(-3) = 1/(3^3) = 1/27.

Front

Evaluate (-8)^2.

Back

(-8)^2 = 64.

Front

What is the result of f(3) if f(x) = (-5)^x?

Back

f(3) = (-5)^3 = -125.

Front

What is the general form of an exponential decay function?

Back

An exponential decay function can be expressed as f(x) = a * e^(-bx), where 'a' is the initial value, 'b' is a positive constant, and 'e' is the base of the natural logarithm.

Front

What happens to the value of an exponential function as x approaches infinity?

Back

As x approaches infinity, the value of an exponential function f(x) = a * b^x (where b > 1) approaches infinity.

Front

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.