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

Front

What is the general form of an exponential function?

Back

The general form of an exponential function is f(x) = a * b^x, where a is the initial value and b is the growth (b > 1) or decay (0 < b < 1) factor.

Front

How do you find 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

Evaluate f(0) for the function f(x) = 3 * 2^x.

Back

f(0) = 3 * 2^0 = 3 * 1 = 3.

Front

What does it mean for an exponential function to have a base greater than 1?

Back

If the base b > 1, the function represents exponential growth, meaning the value of the function increases rapidly as x increases.

Front

What does it mean for an exponential function to have a base between 0 and 1?

Back

If the base 0 < b < 1, the function represents exponential decay, meaning the value of the function decreases rapidly as x increases.

Front

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

Back

To evaluate an exponential function at a specific point x, substitute x into the function and calculate the result.

Front

What is the value of f(1) for the function f(x) = 2 * 5^x?

Back

f(1) = 2 * 5^1 = 2 * 5 = 10.

Front

What is the significance of the initial value 'a' in an exponential function?

Back

The initial value 'a' represents the value of the function when x = 0, which is also the y-intercept.

Front

If f(x) = 4 * 3^x, what is f(2)?

Back

f(2) = 4 * 3^2 = 4 * 9 = 36.