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.

Front

What is the general form of an exponential growth function?

Back

The general form is f(x) = a * b^x, where b > 1.

Front

What is the general form of an exponential decay function?

Back

The general form is f(x) = a * b^x, where 0 < b < 1.

Front

What does the base 'b' represent in an exponential function?

Back

The base 'b' determines the rate of growth or decay. If b > 1, the function represents growth; if 0 < b < 1, it represents decay.

Front

How can you identify exponential growth from a graph?

Back

Exponential growth graphs rise sharply and continuously as x increases, showing a J-shaped curve.

Front

How can you identify exponential decay from a graph?

Back

Exponential decay graphs fall sharply and continuously as x increases, showing a decreasing curve that approaches the x-axis.

Front

What is the effect of changing the value of 'a' in an exponential function?

Back

The value of 'a' represents the initial value or y-intercept of the function. Changing 'a' shifts the graph vertically.

Front

What is the y-intercept of the function f(x) = 3 * 5^(-x)?

Back

The y-intercept is 3, which occurs when x = 0.

Front

What does it mean if a population model is represented by the function 12(1.015)^t?

Back

It indicates that the population is increasing at a rate of 1.5% per year.

Front

What is the difference between exponential growth and linear growth?

Back

Exponential growth increases at a rate proportional to its current value, while linear growth increases by a constant amount.