# Exponential Problem Solving Just remember when exponential functions are involved, functions are increasing or decreasing very quickly (multiplied by a fixed number).That’s why it’s really good to start saving your money early in life and let it grow with time.When $$b) many times by itself, it gets smaller, since the denominator gets larger. Tags: Kumon HomeworkResearch Paper On Language And CultureAnalysis Of DissertationGeneral Essay About MyselfWho Wants To Write My Essay?Review Related Literature ThesisCreative Writing AppA Series Of EssaysPhysics Materials Coursework HelpHelp Me Solve My Math Problems We are going to treat these problems like any other exponential equation with different bases--by converting the bases to be the same. Whether we like it or not, we need to revisit exponents and then start talking about logs, which will help us solve exponential and logarithmic equations. 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. 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.

These are vertical transformations or translations. When transformations are made on the inside of the $$f(x)$$ part, you move the function back and forth (but do the opposite math – basically since if you were to isolate the $$x$$, you’d move everything to the other side).

These are horizontal transformations or translations. When there is a negative sign outside the parentheses, the function is reflected (flipped) across the $$x$$-axis; when there is a negative sign inside the parentheses, the function is reflected across the $$y$$-axis.

In this tutorial, learn how to turn a word problem into an exponential decay function.

$$2^ = 4 \ 8^ = 16 \ \ 16^ = 256 \ \left( \frac \right)^ = 512$$ As you might've noticed, an exponential equation is just a special type of equation.

• ###### Quiz & Worksheet - Solving Exponential Equations

Problem solving - use acquired knowledge to solve an exponential equation practice problem about saving to buy a car using interest from money in the bank Additional Learning…

• ###### Exponentials & Logarithms - Cool math Algebra Help Lessons.

Solving Exponential Equations. Solving for Time and Rates. More Ways to Use This Stuff. Tricks to Help with Solving Log Equations. Solving Log Equations. Exercises…

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Step 6 Finish solving the problem by isolating the variable. Steps for Solving Exponential Equations with the Same Base Step 1 Determine if the numbers can be writ ten using the same base. If so, go to Step 2. If not, stop and use Steps for Solving an Exponential Equation with Different Bases.…

• ###### Working with Exponents and Logarithms - Math Is Fun

Working with Exponents and Logarithms. Always try to use Natural Logarithms and the Natural Exponential Function whenever possible. Solve 2 log 8 x = log 8 16.…

• ###### Exponential Functions and Sequences - rchs.

Chapter 6 Exponential Functions and Sequences Mathematical Practices Problem-Solving Strategies Mathematically profi cient students look closely to fi nd a pattern. Monitoring Progress 1. A rabbit population over 8 consecutive years is given by 50, 80, 128, 205, 328, 524, 839, 1342. Find the population in the tenth year. 2.…

• ###### Solving Exponential and Logarithmic Equations

Solve exponential equations. Solve logarithmic equations. Solve exponential and logarithmic inequalities. Solving Exponential Equations Exponential equations are equations in which variable expressions occur as exponents. The result below is useful for solving certain exponential equations. The preceding property is useful for solving an.…