Population Growth Calculator

Summary

In this MathCelebrity video, Don Sevcik teaches viewers how to calculate population growth using a simple formula: P(t) = P0 * (1 + P)^t, where P0 is the initial population, P is the growth rate, and t is time. He demonstrates the formula with an example of a town with a 10,000 population growing at 5% per year, predicting a future population of approximately 17,959 after 12 years. The video also introduces a population growth calculator on the MathCelebrity website for solving similar problems with different numbers.

Takeaways

• 📚 The video is a tutorial on calculating population growth.
• 🔢 It introduces the formula for population growth: P(t) = P0 * (1 + P)^t, where P0 is the initial population, P is the growth rate, and t is the time.
• ⏱ The formula is used to determine the population at a future date, given the current population, growth rate, and time.
• 📈 The video uses an example with a population of 10,000, a growth rate of 5%, and a time span of 12 years to demonstrate the formula.
• 🧮 The example calculation results in a future population of approximately 17,958, after applying the growth rate and time to the formula.
• 🌐 The video mentions a population growth calculator available on MathCelebrity.com for solving such problems.
• 🔗 A link to the calculator is provided in the video description for easy access.
• 💻 The calculator allows users to input different values for initial population, growth rate, and time to find the future population.
• 🔄 The calculator is flexible, enabling users to change input values and get recalculated results instantly.
• 📈 The video emphasizes the importance of understanding and applying the population growth formula for various scenarios and encourages practice with the calculator.

Q & A

What is the main topic of the video?

The main topic of the video is how to determine population growth using a mathematical formula.

Who is the presenter of the video?

The presenter of the video is Don Sevcik, the founder of MathCelebrity.

What are the three items required to solve a population growth problem according to the video?

The three items required are the current population (P0), the growth rate as a percentage, and the time from now in years, months, or days.

What does the variable 't' represent in the population growth formula?

In the population growth formula, 't' represents the time, which can be in years, months, or days.

What is the formula used to calculate the population at a future date?

The formula used to calculate the population at a future date is P(t) = P0 * (1 + P)^t, where P0 is the initial population, P is the growth rate in decimal form, and t is the time.

What is the example problem presented in the video?

The example problem is to calculate the population of a town 12 years from now, given an initial population of 10,000 and a growth rate of 5% per year.

What is the result of the example problem in the video?

The result of the example problem is that the population 12 years from now will be approximately 17,958 to 17,959, after rounding.

How does the video suggest rounding the final population number?

The video suggests rounding the final population number to the nearest whole number, considering the decimal part of the result.

What is the purpose of the population growth calculator mentioned in the video?

The purpose of the population growth calculator is to allow users to input their own numbers and get the calculated future population based on the provided formula.

How can viewers access the population growth calculator mentioned in the video?

Viewers can access the population growth calculator by visiting the MathCelebrity site or by following a link provided in the video description on YouTube.

What is the advantage of using the population growth calculator over manually plugging in numbers?

The advantage of using the population growth calculator is that it allows for easy swapping of numbers to match different problems without having to manually recalculate each time.

Outlines

00:00

📈 Introduction to Population Growth Calculation

Don Sevcik from MathCelebrity.com introduces a video tutorial on calculating population growth. He explains that population growth problems typically ask for the future population given the current population (P0), growth rate percentage, and time in years, months, or days. The population growth formula is presented as P(t) = P0 * (1 + P)^t, where P(t) is the population at time t, P0 is the initial population, P is the growth rate in decimal form, and t is the time. An example problem is provided where a town with a population of 10,000 grows at a rate of 5% per year, and the calculation is demonstrated to find the population after 12 years. The result is 17,958.56, which is rounded to either 17,958 or 17,959 depending on rounding rules. Don emphasizes the importance of understanding the formula and the steps involved to solve for the future population.

05:01

🔍 Utilizing the Population Growth Calculator

The second paragraph demonstrates the use of the population growth calculator available on the MathCelebrity website. It shows how to input different values into the calculator to solve for the population at a future date. The example given involves an initial population of 12,000 with a 5% growth rate over 12 years. The calculator is used to find the new population, which is then compared to a different problem with an initial population of 15,000, a 6% growth rate, and a time span of 17 years. The video script highlights the flexibility of the calculator, which can be used to solve various population growth problems by simply changing the input values. The tutorial concludes with a thank you note to the viewers and an anticipation for the next video.

Keywords

💡Population Growth

Population growth refers to the increase in the number of individuals in a population over time. In the context of the video, it is the central theme where the presenter, Don Sevcik, explains how to calculate the future population size given the current population, growth rate, and time. The video uses a town with a population of 10,000 as an example to demonstrate the calculation, highlighting the importance of understanding population dynamics.

💡Current Population (P Sub-Zero or P Node)

The current population, denoted as P Sub-Zero or P Node in the video, is the starting point for calculating population growth. It represents the number of individuals at the present time, which serves as a baseline for predicting future population sizes. In the script, the current population of the town is given as 10,000, which is the initial value used in the population growth formula.

💡Growth Rate

The growth rate is a percentage that indicates the expected increase in population over a specified period. It is a critical component in population growth calculations, as it helps determine how quickly the population will expand. In the video, a growth rate of 5% per year is used to illustrate the calculation, showing how this rate affects the future population size.

💡Time (t)

Time, represented by 't' in the video, is the period over which the population growth is measured, such as years, months, or days. It is an essential variable in the population growth formula, as it dictates the duration of growth. The script uses 12 years as an example to show how the population changes over a specific time frame.

💡Population Growth Formula

The population growth formula is a mathematical expression used to calculate the future population size based on the current population, growth rate, and time. The formula presented in the video is P(t) = P0 * (1 + P)^t, where P0 is the initial population, P is the growth rate as a decimal, and t is the time. This formula is central to the video's educational content, as it provides a method for predicting population changes.

💡Decimal Form

Decimal form is the representation of numbers using base-10, which is necessary for mathematical calculations, especially in formulas. In the context of the video, the growth rate of 5% is converted to its decimal form (0.05) for use in the population growth formula. This conversion is essential for accurately calculating the future population.

💡Growth Factor

The growth factor in the video refers to the result of raising (1 + P) to the power of t, where P is the growth rate and t is the time. It is a multiplier used to determine the increase in population size over time. For instance, when the growth factor 1.795856 is multiplied by the initial population of 10,000, it gives the population at time t, which is 17,958.56.

💡Rounding

Rounding is the process of approximating a number to a certain level of precision, often to the nearest whole number. In the video, after calculating the future population as 17,958.56, the presenter rounds the number to either 17,958 or 17,959, depending on the context or the need for a whole number. Rounding is a common practice in population studies to simplify results.

💡Population Growth Calculator

The population growth calculator mentioned in the video is a tool that simplifies the process of calculating future population sizes. It allows users to input their specific values for initial population, growth rate, and time, and then automatically calculates the future population using the population growth formula. The calculator is showcased as a practical application of the formula discussed in the video, making it easier for viewers to apply the concept to different scenarios.

💡Percentage

A percentage is a way of expressing a number as a fraction of 100, which is useful for representing proportions or rates, such as the growth rate in population studies. In the video, the growth rate is given as a percentage (5%), which is then converted to a decimal (0.05) for use in the population growth formula. Understanding percentages is crucial for accurately performing calculations in this context.

Highlights

Introduction to the population growth calculator video by MathCelebrity.com

Explanation of population growth and its relevance

Identification of the three key elements for population growth calculation: current population, growth rate, and time

Presentation of the population growth formula

Clarification that the formula can be used to solve for any part of the equation, but typically focuses on future population

Example problem presented: calculating population in 12 years with a 5% growth rate

Step-by-step guide on how to apply the formula using the given example

Conversion of the growth rate percentage to a decimal for calculation purposes

Explanation of how to calculate the growth factor by raising 1 plus the growth rate to the power of time

Multiplication of the growth factor by the initial population to find the future population

Discussion on rounding the final population number to the nearest whole number

Recap of the process to solve for future population using the population growth formula

Introduction of the population growth calculator tool available on MathCelebrity.com

Demonstration of how to use the calculator with different input values

Advantages of the calculator for solving various population growth problems with ease

Encouragement for viewers to try the calculator and explore different scenarios

Conclusion and thanks to viewers for watching the video

Transcripts

(upbeat music)

- [Don] Welcome to the population growth

calculator video from MathCelebrity.com.

My name is Don Sevcik, Founder of MathCelebrity,

and in the next three minutes,

I'm gonna show you how to determine population growth.

So let's talk about population growth.

You'll know that this is a problem for population growth

when they ask for a population at a future date,

given three items.

Current population, we call this P Sub-Zero or P Node.

Growth rate as a percentage,

and finally, a time from now listed in years,

months, days, etcetera

Here is the population growth formula.

Now sometimes I'll ask you to solve four pieces

within the formula,

but generally the want to know a population

at a future date.

That's P of t,

t represents the time

whether it's listed in years, months, or days.

And what we're doing here

is we're taking an initial population at time zero.

We're raising it to one plus P where P as a percentage,

we're adding one plus P

and we're raising that to the t power.

And you'll get your population at time t.

So what this formula and these end points,

let's look at an example.

Here's a problem that you'll often see

for population growth.

A town has a population of 10,000.

The population grows at a rate of 5% per year.

What will the population be in 12 years?

Okay. So we know this problem

wants to know a future population.

Let's take what we're given and see how we solve this.

I'm listing our formula again,

to calculate population growth.

So we're given P Sub Node equals 10,000,

P equals 5% or 0.05 in decimal form,

and t equals 12

and the 12 being years.

And we wanna know

what is P of 12.

So the population 12 years from now given the growth rate.

So let's go ahead and plug in our numbers

and see what we get.

Using the population growth formula

we plug in our numbers,

we simplify, and we get this.

So now we need to evaluate 1.05 raised to the 12th,

which is 1.795856 ,

and we're gonna multiply that growth factor times 10,000.

So our population at time 12 is 17,958.56

And these problems generally want you to round.

In this case,

because it's more than a half of person you can round up.

If there's multiple choice,

I usually look for the closest answer

either 17,958 or 17,959.

So to recap,

you're given three pieces of the population growth formula

you wanna solve for the last one.

And so you take your percentage,

make it a decimal, add one,

raise it to t

and multiply by your initial population

and it gives you your future population.

This is your growth factor.

Now the chances are very strong

that you're gonna run across

more population growth problems.

In fact, you may even be looking at one now,

where the numbers differ

from the example right here.

If that's the case,

do you really wanna mix and match numbers

to match this problem?

Or is there an easier way?

I've created one for you.

If you're on the math celebrity site,

you probably already know

where the population growth calculator is

because the video sits on there.

If you're finding us from YouTube,

I'm gonna show you

how to get to the population growth calculator.

I'll put a link in the description

so you can get there and type your problem in.

So with that being said,

let's take a look at the calculator.

Here is our population growth calculator.

And you essentially enter your problem in this box,

and when you're ready to go,

you just hit solved,

so this is a similar,

similar problem that we covered

there's just a few different numbers.

So let's go ahead.

So we've got a population initial population of 12,000,

a growth rate of 5%

at a time of 12.

We wanna know what the population is at time 12.

So you go add, and it plugs and shrugs with your numbers,

just like we did in the video

and finds your new population.

Now here's, what's fun about this,

let's say your next problem

asks you for initial population of 15,000,

a growth rate of 6%,

and what's the population gonna be in 17 years.

You don't have to type it exactly like this

I'm just giving you an example.

You're gonna hit solve,

and it's gonna recalculate based on your new inputs.

So 15,000 initial population,

6% growth rate,

and time of 17.

It runs through the formula,

calculates your growth factor,

and here is your new population.

So what's nice about this is you can swap out numbers

and it'll just walk you through the exact same

step-by-step formula

to get you to your new population.

I wanna thank you for watching this video

and spending time with me today,

and I will see you in the next video.