Exponential growth and decay word problems calculator

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Enter an initial value, growth rate percent, and total time into the calculator below to determine the total exponential growth at the given time.

Calculator Operations:

• Calculate a final value given the initial value, growth rate, and time.
• Calculate the initial value given the final value, growth rate, and time.
• Calculate the growth rate given the final value, initial value, and time.
• Calculate the time given the initial value, final value, and growth rate.

Exponential Growth Formula

The following formula is used by the calculator above to determine the exponential growth of a value.

x(t) = x0 × (1 + r) t

• Where x(t) is the final value after time t
• x0 is the initial value
• r is the rate of growth in percent
• and t is the total time

Exponential Growth Definition

Exponential growth is defined as the growth of an object or asset that is described or can be modeled by an exponential function like the one above. Exponential functions grow “exponentially” with each step forward.

How to calculate exponential growth?

The following example is a step-by-step guide on determining the total value of a number after some time of exponential growth.

1. First, we must determine the initial value. For this example, we will assume we are looking at an investment going through exponential growth through interest. Let’s assume a value of $1,000.00.
2. The next step is the determine the growth rate r, this would be the interest per time step, so let’s assume interest per month. It will be 10%.
3. The final step is to determine the total time that has passed. We will say 2 years or 24 months.
4. Lastly, enter the information into the formula above to determine your answer.

FAQ

What is exponential growth?

Exponential growth is defined as the growth of an object or asset that is described or can be modeled by an exponential function.

2 number Word Problems

This calculator handles word problems in the format below:
* Two numbers have a sum of 70 and a product of 1189 What are the numbers?
* Two numbers have a sum of 70. Their difference 32

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2 Unknown Word Problems

Solves a word problem based on two unknown variables

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Age Difference

Determines the ages for an age difference word problem.

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Age Word Problems

Determines age in age word problems

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Angle of Elevation

Solves angle of elevation word problems

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Break Even

Given a fixed cost, variable cost, and revenue function or value, this calculates the break-even point

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Coin Combinations

Given a selection of coins and an amount, this determines the least amount of coins needed to reach that total.

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Coin Total Word Problems

This word problem lesson solves for a quantity of two coins totaling a certain value with a certain amount more or less of one coin than another

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Coin Word Problems

This word problem lesson solves for a quantity of two coins totaling a certain value

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Collinear Points that form Unique Lines

Solves the word problem, how many lines can be formed from (n) points no 3 of which are collinear.

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Compare Raises

Given two people with a salary and annual raise amount, this determines how long it takes for the person with the lower salary to catch the person with the higher salary.

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Consecutive Integer Word Problems

Calculates the word problem for what two consecutive integers, if summed up or multiplied together, equal a number entered.

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Cost Revenue Profit

Given a total cost, variable cost, revenue amount, and profit unit measurement, this calculates profit for each profit unit

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Decay

Determines decay based on an initial mass and decay percentage and time.

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Distance Catch Up

Calculates the amount of time that it takes for a person traveling at one speed to catch a person traveling at another speed when one person leaves at a later time.

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Distance Rate and Time

Solves for distance, rate, or time in the equation d=rt based on 2 of the 3 variables being known.

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Find two numbers word problems

Given two numbers with a sum of s where one number is n greater than another, this calculator determines both numbers.

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Inclusive Number Word Problems

Given an integer A and an integer B, this calculates the following inclusive word problem questions:
1) The Average of all numbers inclusive from A to B
2) The Count of all numbers inclusive from A to B
3) The Sum of all numbers inclusive from A to B

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Map Scale

Solves map scale problems based on unit measurements

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Markup Markdown

Given the 3 items of a markup word problem, cost, markup percentage, and sale price, this solves for any one of the three given two of the items. This works as a markup calculator, markdown calculator.

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Numbers Word Problems

Solves various basic math and algebra word problems with numbers

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Overtime

Solves overtime wage problems

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Percent Off Problem

Given the 3 items of a percent word problem, Reduced Price, percent off, and full price, this solves for any one of the three given two of the items.

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Percentage of the Pie Word Problem

This takes two or three fractions of ownership in some good or object, and figures out what remaining fraction is left over.

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Percentage Word Problems

Solves percentage word problems

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Population Doubling Time

Determines population growth based on a doubling time.

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Population Growth

Determines population growth based on an exponential growth model.

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Product of Consecutive Numbers

Finds the product of (n) consecutive integers, even or odd as well. Examples include:
product of 2 consecutive integers
product of 2 consecutive numbers
product of 2 consecutive even integers
product of 2 consecutive odd integers
product of 2 consecutive even numbers
product of 2 consecutive odd numbers
product of two consecutive integers
product of two consecutive odd integers
product of two consecutive even integers
product of two consecutive numbers
product of two consecutive odd numbers
product of two consecutive even numbers
product of 3 consecutive integers
product of 3 consecutive numbers
product of 3 consecutive even integers
product of 3 consecutive odd integers
product of 3 consecutive even numbers
product of 3 consecutive odd numbers
product of three consecutive integers
product of three consecutive odd integers
product of three consecutive even integers
product of three consecutive numbers
product of three consecutive odd numbers
product of three consecutive even numbers
product of 4 consecutive integers
product of 4 consecutive numbers
product of 4 consecutive even integers
product of 4 consecutive odd integers
product of 4 consecutive even numbers
product of 4 consecutive odd numbers
product of four consecutive integers
product of four consecutive odd integers
product of four consecutive even integers
product of four consecutive numbers
product of four consecutive odd numbers
product of four consecutive even numbers
product of 5 consecutive integers
product of 5 consecutive numbers
product of 5 consecutive even integers
product of 5 consecutive odd integers
product of 5 consecutive even numbers
product of 5 consecutive odd numbers
product of five consecutive integers
product of five consecutive odd integers
product of five consecutive even integers
product of five consecutive numbers
product of five consecutive odd numbers
product of five consecutive even numbers

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Ratio Word Problems

Solves a ratio word problem using a given ratio of 2 items in proportion to a whole number.

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Rebound Ratio

Calculates a total downward distance traveled given an initial height of a drop and a rebound ratio percentage

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Slope Word Problems

Solves slope word problems

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Solution Mixture

Determines a necessary amount of a Solution given two solution percentages and 1 solution amount.

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Split Fund Interest

Given an initial principal amount, interest rate on Fund 1, interest rate on Fund 2, and a total interest paid, calculates the amount invested in each fund.

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Sum of Consecutive Numbers

Finds the sum of (n) consecutive integers, even or odd as well. Examples include:
sum of 2 consecutive integers
sum of 2 consecutive numbers
sum of 2 consecutive even integers
sum of 2 consecutive odd integers
sum of 2 consecutive even numbers
sum of 2 consecutive odd numbers
sum of two consecutive integers
sum of two consecutive odd integers
sum of two consecutive even integers
sum of two consecutive numbers
sum of two consecutive odd numbers
sum of two consecutive even numbers
sum of 3 consecutive integers
sum of 3 consecutive numbers
sum of 3 consecutive even integers
sum of 3 consecutive odd integers
sum of 3 consecutive even numbers
sum of 3 consecutive odd numbers
sum of three consecutive integers
sum of three consecutive odd integers
sum of three consecutive even integers
sum of three consecutive numbers
sum of three consecutive odd numbers
sum of three consecutive even numbers
sum of 4 consecutive integers
sum of 4 consecutive numbers
sum of 4 consecutive even integers
sum of 4 consecutive odd integers
sum of 4 consecutive even numbers
sum of 4 consecutive odd numbers
sum of four consecutive integers
sum of four consecutive odd integers
sum of four consecutive even integers
sum of four consecutive numbers
sum of four consecutive odd numbers
sum of four consecutive even numbers
sum of 5 consecutive integers
sum of 5 consecutive numbers
sum of 5 consecutive even integers
sum of 5 consecutive odd integers
sum of 5 consecutive even numbers
sum of 5 consecutive odd numbers
sum of five consecutive integers
sum of five consecutive odd integers
sum of five consecutive even integers
sum of five consecutive numbers
sum of five consecutive odd numbers
sum of five consecutive even numbers

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Sum of Five Consecutive Integers

Finds five consecutive integers, if applicable, who have a sum equal to a number. Sum of 5 consecutive integers

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Sum of Four Consecutive Integers

Finds four consecutive integers, if applicable, who have a sum equal to a number. Sum of 4 consecutive integers

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Sum of the First (n) Numbers

Determines the sum of the first (n)
* Whole Numbers
* Natural Numbers
* Even Numbers
* Odd Numbers
* Square Numbers
* Cube Numbers
* Fourth Power Numbers

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Sum of Three Consecutive Integers

Finds three consecutive integers, if applicable, who have a sum equal to a number. Sum of 3 consecutive integers

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Sun Shadow

This solves for various components and scenarios of the sun shadow problem

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Unit Savings

A discount and savings word problem using 2 people and full prices versus discount prices.

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Work Word Problems

Given Person or Object A doing a job in (r) units of time and Person or Object B doing a job in (s) units of time, this calculates how long it would take if they combined to do the job.

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How do you write an equation for exponential growth and decay?