Exponential Equations

Front

What is an exponential equation?

Back

An exponential equation is a mathematical expression in which a variable appears in the exponent. It can be written in the form y = ab^x, where a is a constant, b is the base, and x is the exponent.

Front

What does the base in an exponential function represent?

Back

The base in an exponential function represents the growth (if greater than 1) or decay (if between 0 and 1) factor of the function.

Front

What is the general form of an exponential growth equation?

Back

The general form of an exponential growth equation is y = ab^x, where b > 1.

Front

What is the general form of an exponential decay equation?

Back

The general form of an exponential decay equation is y = ab^x, where 0 < b < 1.

Front

In the equation P = 6191(1.04)^t, what does the 1.04 represent?

Back

The 1.04 represents a 4% annual increase in population.

Front

How do you find the initial value in an exponential equation?

Back

The initial value can be found by evaluating the equation at x = 0, which gives y = a.

Front

What is the value of b in the equation y = ab^x if the quantity decreases by 29% each hour?

Back

The value of b is 0.71, representing a 29% decrease.

Front

What is the population in 1990 if P = 6191(1.04)^t and t = 0?

Back

The population in 1990 is 6191.

Front

What type of function is y = 7(5/4)^x?

Back

This is an example of an exponential growth function.

Front

What does it mean if an exponential function has a base greater than 1?

Back

If the base is greater than 1, the function represents exponential growth.