MCLA - 7.3-7.5 - 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 in an exponential function is the factor by which the function's value changes for each unit increase in the exponent. It is represented by the base 'b' in the function f(x) = a(b)^x.

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

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the base 'b' is greater than 1, leading to increasing values as x increases. Exponential decay occurs when the base 'b' is between 0 and 1, leading to decreasing values as x increases.

Front

What does the base of an exponential function represent?

Back

The base of an exponential function determines the rate of growth or decay. A base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

Front

If f(x) = 2(4)^x, what is the common ratio?

Back

The common ratio is 4.

Front

What is the y-intercept of the function f(x) = 2(4)^x?

Back

The y-intercept is 2.

Front

What type of function is f(x) = 2(1/7)^x?

Back

It is an exponential decay function.

Front

If a population is modeled by f(x) = 800(0.87)^x, what is the percentage decay?

Back

The percentage decay is 13%.

Front

What does it mean if a graph shows exponential growth?

Back

It means that the values of the function increase rapidly as x increases, indicating a growth pattern.