What makes an exponential equation

Connect the points as best you can, using a smooth curve not a series of straight lines. Use the shape of an exponential graph to help you: this graph gets very close to the. This is an example of exponential growth. Start with a table of values. Notice that the larger base in this problem made the function value skyrocket.

Even with x as small as 2, the function value is too large for the axis scale you used before. You can change the scale, but then our other values are very close together. Because you know the square root of 4, you can find that value in this case:. The point is the blue point on this graph. For other bases, you might need to use a calculator to help you find the function value.

Use the shape of an exponential graph to help you: this graph gets very close to the x -axis on the left, but never really touches the. Notice that a larger base makes the graph steeper.

All the graphs go through 0, 1! Exponential Decay. Be careful with the negative exponents! Remember to take the reciprocal of the base to make the exponent positive.

In this case, , and. Use the table as ordered pairs and plot the points. Connect the points as best you can using a smooth curve not a series of straight lines. This is exponential decay. They get closer and closer to 0. Create a table of values. Again, be careful with the negative exponents. Notice that in this table, the x values increase. The y values decrease. Use the table pairs to plot points.

Note that the bases are not the same. But we can rewrite 64 as a base of 4. Rewrite 64 as 4 3 so each side has the same base. By the property of equality of exponential functions, if the bases are the same, then the exponents must be equal. The equality property of exponential equations says to set the exponents equal whenever the bases on both sides of the equation are equal. When an exponential equation has the same bases on both sides, just set the exponents equal and solve for the variable.

Here the bases on both sides are equal. So we can set the exponents also equal. When an exponential equation has different bases on both sides, apply log on both sides and solve for the variable. Learn Practice Download. Exponential Equations Exponential equations, as their name suggest, involve exponents. What Are Exponential Equations? Exponential Equations Formulas 3.

We can make the bases to be the same on both sides using this. So we can set the exponents to be equal. Solution: cannot be written as a power of 7.

The range is all real numbers greater than zero. Exponential functions have special applications when the base is e. Its decimal approximation is about 2. Go ahead and plug the equation into your calculator and check it out.