Exponential Problem Solving

It's an equation that has exponents that are $$ \red$$.

$$ \red 4^3 = \red 2^x $$ $$ \red 9^x = \red $$ $$ \left( \red \right)^ = \red 4^3 $$ $$ \red 4^ 1 = \red $$ In each of these equations, the base is different.

These types of equations are used in everyday life in the fields of Banking, Science, and Engineering, and Geology, as well as more fields.

We learned about the properties of exponents here in the Exponents and Radicals in Algebra Section, and did some solving with exponents here.

Check out these kinds of exponential functions in this tutorial!

If something decreases in value at a constant rate, you may have exponential decay on your hands.

Exponential functions often involve the rate of increase or decrease of something.

When it's a rate of increase, you have an exponential growth function!

Remember that exponential functions are named that because of the “\(x\)” in their exponents! “\(b\)” is called the base of the exponential function, since it’s the number that is multiplied by itself “\(x\)” times (and it’s not an exponential function when \(b=1\)).

\(b\) is also called the “growth” or “decay” factor.

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