Exponential - quadratic equation

Thread starter Tom83B
Start date Sep 13, 2010
Tags

Exponential Quadratic Quadratic equation

In summary, an exponential-quadratic equation is a combination of exponential and quadratic functions, written in the form y = a*b^x + c*x^2. It differs from a regular quadratic equation in that it has both an exponential and quadratic term, resulting in a curved shape when graphed. Real-life applications of this type of equation include modeling population growth, financial investments, and motion in physics. To solve an exponential-quadratic equation, various methods such as graphing, factoring, completing the square, or using the quadratic formula can be used. The constants in the equation determine the behavior and characteristics of the graph, with a affecting the overall shape, and b and c determining the location and direction of the curve.

Sep 13, 2010

Tom83B

Homework Statement

2ⁿ=n²

Homework Equations

The Attempt at a Solution

I know the solution is 2 and 4. But I have no idea how to solve it without guessing...

Physics news on Phys.org

Sep 13, 2010

Jolsa

Try looking at the LambertW function :) There's actually a third solution apart from the two you already found, its about -0.767

What is an exponential-quadratic equation?

An exponential-quadratic equation is a type of equation that combines both exponential and quadratic functions. It can be written in the form y = a*b^x + c*x^2, where a, b, and c are constants and x is the variable.

What is the difference between an exponential-quadratic equation and a regular quadratic equation?

An exponential-quadratic equation has both an exponential and a quadratic term, while a regular quadratic equation only has a quadratic term. This means that an exponential-quadratic equation will have a curved shape, rather than a parabola, when graphed.

What are some real-life applications of exponential-quadratic equations?

Exponential-quadratic equations can be used to model various real-life phenomena, such as population growth, financial investments, and the spread of diseases. They can also be used in physics to describe the motion of objects under the influence of both exponential and quadratic forces.

How do you solve an exponential-quadratic equation?

To solve an exponential-quadratic equation, you can use a variety of methods such as graphing, factoring, completing the square, or using the quadratic formula. The specific method used will depend on the form of the equation and the given information.

What is the significance of the constants in an exponential-quadratic equation?

The constants in an exponential-quadratic equation determine the behavior and characteristics of the graph. The constant a affects the overall shape of the curve, while b and c determine the location of the vertex and the direction of the curve, respectively.