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## Course: Algebra 2 > Unit 12

## Exponential equation word problem

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## How to Write an Exponential Function: Word Problems

## A step-by-step guide to Writing exponential function: word problems

Variable \(y\): represents the output value

\(a\) represents the initial value

\(b\) represents the common ratio

\(x\) represents the number of times the original value has been multiplied by the common ratio

Follow the step-by-step procedure below to write an exponential function.

Step \(2\): Using the variables, write the exponential function in the form of \(y=ab^x\).

Step \(6\): Place the values of \(a\), \(b\) and \(x\) in the exponential function and simplify it.

Step \(7\): Check your work by inserting \(x\) values and seeing if they match the problem statement

Step \(8\): Write the final answer in one sentence

## Writing exponential function: word problems-Example 1:

by: Effortless Math Team about 5 months ago (category: Articles )

## Effortless Math Team

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## How Do You Solve a Word Problem Using an Exponential Function?

## Background Tutorials

Factors and greatest common factor.

## What's a Factor?

## Function Definitions and Notation

## What's a Function?

## Evaluating Expressions

## How Do You Evaluate an Algebraic Expression?

## What is a Variable?

## Rules of Exponents

## What are Exponents?

## Prime Factorization

## How Do You Find the Prime Factorization of a Number Using a Tree?

## Further Exploration

## How Do You Graph an Exponential Function Using a Table?

## Modeling with Exponential Functions

## How Do You Identify Exponential Behavior from a Pattern in the Data?

## Exponential Functions

## Introduction to Exponential Functions

## Parent Graphs of Exponential Functions

## Transformations of Exponential Functions

Domain : \(\left( {-\infty ,\infty } \right)\)

Range : \(\left( {3,\infty } \right)\)

Translate 4 units right, 3 units up.

Remember that \(e\approx 2.7\).

Since the coefficient is negative, the graph is reflected (flipped) across the \(x\)-axis.

Domain : \(\left( {-\infty ,\infty } \right)\)

Range : \(\left( {-\infty ,2} \right)\)

Vertical stretch by a factor of 2 , reflect over the \(x\)-axis, translate 1 unit left, 2 units up.

## Writing Exponential Equations from Points and Graphs

You may be asked to write exponential equations, such as the following:

- Write an equation to describe the exponential function in form \(y=a{{b}^{x}}\), with a given base and a given point.
- Write an exponential function in form \(y=a{{b}^{x}}\) whose graph passes through two given points. (You may be able to do this using Exponential Regression .)
- For a certain graph, write the appropriate exponential function of the form \(y=a{{b}^{x}}+k\), given an asymptote.
- For a certain graph, write the appropriate exponential function of the form \(y=a{{b}^{{x-h}}}+k\), given a certain base and asymptote.
- For a certain exponential function \(f\left( x \right)=a{{b}^{{x-h}}}+k\), the new \((0, 1)\) reference point is \(\left( {h,a+k} \right)\), if you’re only asked for this point. Also, to find the “\(a\)”, given an exponential graph and a transformed reference point, you can subtract the \(y\)-value of the asymptote (\(k\)) from the \(y\)-value of the new reference point (\(a=\left( {a+k} \right)-k\)).

## Exponential Function Applications and Word Problems

## Continuous Compounding

## More Growth/Decay Equations

There are two more exponential equations that are a little more specific:

Here are all the exponential formulas we’ve learned:

Remember when we put an exponent in the Graphing Calculator, we just use the “^” key!

## Half-Life Problems:

## Why Use Logs?

In about 4.6 years, there will be less than 300 students . See how difficult this is?

## Solving Exponential Functions by Matching Bases

(We will also see another common way to solve equations with variables in exponents – logarithms !)

## Exponential Regression

## Exponential Inequalities

Let’s do an inequality problem:

Learn these rules, and practice, practice, practice!

On to Logarithmic Functions – you are ready!

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## Exponential-Growth Word Problems

Log Probs Expo Growth Expo Decay

## What is the formula for exponential growth?

## MathHelp.com

A = P e r t A = P e k t Q = N e k t Q = Q 0 e k t

## How do you solve exponential growth problems?

## What is an example of an exponential growth problem?

The beginning amount P is the amount at time t = 0 , so, for this problem, P = 100 .

The ending amount is A = 450 at t = 6 hours.

ln(4.5) / 6 = k = 0.250679566129...

I know that the starting population is P = 100 , and I need to find A at time t = 36 .

But what is the growth constant k ? And why do they tell me what the doubling time is?

At this point, I need to use logs to solve:

A = 100 e 36(ln(2)/6.5) = 4647.75313957...

The answer I got above, 4678 bacteria in thirty-six hours, fits nicely between these two estimates.

100 × 2 (72/13) = 4647.75314...

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## IMAGES

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## COMMENTS

Whether you love math or suffer through every single problem, there are plenty of resources to help you solve math equations. Skip the tutor and log on to load these awesome websites for a fantastic free equation solver or simply to find an...

According to the University of Regina, another way to express solving for y in terms of x is solving an equation for y. The solution is not a numerical value; instead, it is an expression equal to y involving the variable x. An example prob...

The four steps for solving an equation include the combination of like terms, the isolation of terms containing variables, the isolation of the variable and the substitution of the answer into the original equation to check the answer.

That could be the fastest way for many people, and it's extra nice because you don't necessarily need a calculator to solve it. Sal's way works best for me (

In this video we learn how to solve exponential function word problems. We create the equation by converting the percentage growth/decay

How to solve word problems involving exponential functions.

Exponential functions are characterized by the fact that the growth rate of the function is proportional to the function's current value.

In this tutorial, learn how to turn a word problem into an exponential growth function. Then, solve the function and get the answer!

How Do You Solve a Word Problem Using an Exponential Function? Note: Word problems let you see math in the real world! This tutorial shows you how to create a

In this section, you will: review strategies for solving equations arising from exponential formulas; solve application problems involving

In some cases, we have to solve equations that include an exponential function where the base of the function is the variable.

Exponential Function Applications and Word Problems · Continuous Compounding · More Growth/Decay Equations · Half-Life Problems: · Why Use Logs?

a) Write an equation that expresses the number of beetles at time x.

To solve exponential growth word problems, you may be plugging one value into the exponential-growth equation, and solving for the required result.