#### What is an exponential equation

## What is an example of an exponential equation?

Exponential equations are equations in which variables occur as exponents. For example, exponential equations are in the form ax=by . To solve exponential equations with same base, use the property of equality of exponential functions . If b is a positive number other than 1 , then bx=by if and only if x=y .

## What defines an exponential function?

An exponential function is a mathematical function of the following form: f ( x ) = a ^{x}. where x is a variable, and a is a constant called the base of the function. The most commonly encountered exponential-function base is the transcendental number e , which is equal to approximately 2.71828.

## What does an exponential equation look like?

Exponential functions have the form f(x) = b^{x}, where b > 0 and b ≠ 1. Just as in any exponential expression, b is called the base and x is called the exponent. An example of an exponential function is the growth of bacteria. Some bacteria double every hour.

## How do you tell if a graph is an exponential function?

Graphs of Exponential FunctionsThe graph passes through the point (0,1)The domain is all real numbers.The range is y>0.The graph is increasing.The graph is asymptotic to the x-axis as x approaches negative infinity.The graph increases without bound as x approaches positive infinity.The graph is continuous.

## How do you determine if a function is exponential or linear?

If the y values are also increasing at a constant rate then your function is linear. In other words, a function is linear if the difference between terms is the same. For exponential functions the difference between terms will not be the same. However, the ratio of terms is equal.

## How do you solve an exponential function?

To solve an exponential equation, take the log of both sides, and solve for the variable. Ln(80) is the exact answer and x=4.38202663467 is an approximate answer because we have rounded the value of Ln(80).. Check: Check your answer in the original equation.

## What do A and B mean in an exponential equation?

The parameter a is called the function’s y-intercept and the parameter b is called the base. Together, they completely determine an exponential function’s input-output behavior. Notice that f(0) = ab^{} = a1 = a : The y-intercept is the output when the input is 0.

## What are the parts of an exponential equation?

In an exponential function, the independent variable, or x-value, is the exponent, while the base is a constant. For example, y = 2x would be an exponential function. Here’s what that looks like. The formula for an exponential function is y = abx, where a and b are constants.