Exponential Functions Review

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. It represents growth or decay processes.

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 determines how much the function grows or decays with each unit increase in '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). This gives the initial value 'a'.

Front

What does a base greater than 1 indicate in an exponential function?

Back

A base greater than 1 indicates exponential growth. As 'x' increases, the function's value increases rapidly.

Front

What does a base between 0 and 1 indicate in an exponential function?

Back

A base between 0 and 1 indicates exponential decay. As 'x' increases, the function's value decreases rapidly.

Front

How do you express a percentage increase in an exponential function?

Back

To express a percentage increase in an exponential function, use the form f(x) = a(1 + r)^x, where 'r' is the percentage increase expressed as a decimal.

Front

What is the formula for exponential decay?

Back

The formula for exponential decay is f(x) = a(1 - r)^x, where 'a' is the initial amount and 'r' is the decay rate expressed as a decimal.

Front

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

Back

The initial value in an exponential function represents the starting amount before any growth or decay occurs. It is the value of the function when x = 0.

Front

How can you determine if a graph represents growth or decay?

Back

A graph represents growth if it rises as x increases and decay if it falls as x increases. The base of the function also indicates this: base > 1 for growth, base < 1 for decay.

Front

What is the relationship between the base and the growth factor in an exponential function?

Back

The growth factor in an exponential function is the base 'b'. If the function is in the form f(x) = a(b)^x, then 'b' determines how quickly the function grows.