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Published on April 22, 2020

Understand the 2 Types of Growth Curves to Grow Faster

Understand the 2 Types of Growth Curves to Grow Faster

When someone last talked to you about logarithmic and exponential growth curves, you probably had flashbacks to that math class you took in high school. Whether those are good or bad memories for you doesn’t matter because we aren’t talking about mathematical calculations today.

Today, the growth curves we’re talking about have everything to do with your personal development and growth.

What Are the 2 Types of Growth Curves?

The two types of growth curves that are most common are logarithmic growth curves and exponential growth curves. Essentially, they are the opposite of each other.

I’ll start by explaining and exponential growth curve as that is the one people are typically more familiar with.

Exponential Growth Curves

An exponential growth curve is one where the slope of the curve gets greater and greater as you move along it.[1] The best way to imagine an exponential curve, if you don’t know what it looks like, is to think about an investment portfolio.

Over time your investments grow in value, and due to the compound interest, year after year you are making more money than you made the previous year. For example, say you invested $100 and got a 10% return. At the end of the year, you’d have $110. Now next year say you again got a 10% return, but now you have the $110 in the account. This would mean you gained $11 this year, $1 more than the previous year. Over time, this gap between years gets larger and larger, and the slope of the curve gets steeper and steeper!

Now let’s talk a little bit about the logarithmic growth curves.

Logarithmic Growth Curves

A logarithmic growth curve is essentially the opposite of an exponential growth curve. In a logarithmic growth curve, the curve of the line starts by going up very stteply, and then over time the slope of the line continually declines until it becomes essentially flat.

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Try to picture this like you were starting a 100m sprinting race. If you started from a standstill and then took off with the gunshot, your speed would rapidly increase for the first few seconds. However, as you approached the 30-50m mark, you would be running pretty fast, so it would be harder to run even faster, but you still could if you tried. Now by the time you get to the 80m mark, you’re probably running at just about max speed for you, and no matter how hard you ty, any increases in your speed from here will be minimal.

There are two examples of the types of curves that we’ll be talking about in terms of personal development and growth today.[2] Let’s shift our talk today over to how this information can help you moving forward!

How Understanding Growth Curves Benefits Your Development

They always say that knowledge is power. I believe that this is partly true. I much prefer to think of knowledge as potential power. You could have all the knowledge in the world, but if you don’t know how or fail to apply that knowledge, then what good is it to you?

So let’s explore how understanding each type of growth curve could benefit you as you travel through your personal development and growth journey.

Understanding Exponential Growth Curves

As we discussed, exponential growth curves are ones where the slope of the curve increases at an ever-steepening rate. We applied the example of an investment portfolio here.

However, this is very applicable to your growth journey as well.

Have you ever noticed that as you continually practice certain skills, you get better and better at performing them? Of course you have. That’s pretty common knowledge; as you practice something, you get better and better at it.

Some skills will undergo exponential growth or lead to exponential growth in certain areas of your life.

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The example that comes to mind is that of entrepreneurship. They say that making the first million in any business is always the hardest. Why is that? Because it takes time to develop and gain experience to make that first million. You have to learn the lessons and develop the skills that allow you to achieve this goal.

So what do you think happens when you go to make your second million after you’ve already made your first? Do you think that it will take less time or more time? It will take less time, right? You’ve already developed the skills and gained the experiences you need to achieve this goal.

Therefore, over time, your returns will get greater and greater as you work on these skills.

Why is this important?

This is important because it shows us that for skills with exponential growth, there is a significant learning curve at the outset, but over time, as we develop these skills, things get easier and easier and our returns get greater and greater!

Understanding this growth curve can remind us that things won’t always come easily to us, that you need to put in the work upfront to achieve these goals, but after you’ve put in that significant amount of upfront work, your efforts begin to pay you back in dividends long-term.

Understanding Logarithmic Growth Curves

Remember that logarithmic growth curves are essentially the opposite in appearance to exponential growth curves. The slope of the curve is very steep at the beginning, but the slope slowly declines over time until the line becomes essentially flat.

A real-life example of this could be seen in top-level athletes and the work they put into their sport and physical abilities or people who are studying for examinations as they try to learn and consume material.

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Let’s start with the student.

Any student will tell you that the difference between getting 50% on an exam and 70% is not that significant. That’s a jump of 20%. However, they’ll also tell you that the difference in effort required to get 90% versus 95% is often massive. That’s a jump of only 5% this time, but the effort to make that jump is much higher than the initial 20% jump completed earlier.

Athletes experience similar cases in regards to their physical performance. Let’s talk about sprinter again. When you first start training for sprinting, you’re probably pretty slow. However, as you practice and learn the proper form, you’re able to cut 5 seconds off your 200m sprint time in just a few weeks without too much effort. Then, as you keep practicing and perfecting your technique, you can shave off another few seconds as you become more masterful. However, once you reach elite levels of sprinting, the effort and dedication that it takes to shave off even just 1 second, or maybe even less, is truly immense!

So why is understanding this growth curve important?

What understanding this curve can teach us is that to reach truly elite levels of performance of certain skills, we are going to have to work hard. Yes, you are going to see lots of improvement at the outset, but over time as you progress, it’s going to become harder and harder to reach that next level.

You need to ask yourself if are you willing to put in the work to reach those levels on your development journey. Are you willing to work harder than everybody else? Are you willing to work like the top 1% to be the top 1%?

Putting It All Together

Now that you understand the different growth curves and how they can be applied to your life, let’s talk about the critical pieces of information to take away from this article.

The important thing to understand in regards to growth curves for personal development is to identify which curve is likely going to apply to the skill you’re developing so you can prepare yourself mentally for the challenges that you’re inevitably going to have to face.

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For example, let’s take exponential skills as our first example. We know that the growth we see in these skills early on is minimal. It’s later in the process that you see the fruits of your labors. Therefore, you should prepare yourself mentally for the early frustrations you’re likely to experience.

Understand that even though you aren’t seeing much progress upfront, the effort you’re putting in now is towards a much larger goal and return later.

Now let’s look at logarithmic skills. These are the opposite. Here the growth is fast initially, but over time the returns of your efforts dwindle as you approach elite levels. Now the challenge is flipped. Now you have to do your best to not let your ego get too big as your growth skyrockets initially, and you also have to prevent yourself from getting discouraged later in the process when growth becomes increasingly more difficult.

Apply these lessons to your life. Mentally prepare yourself for the challenges that lay ahead of you. If you can master the mind on your course to personal development, you’ve already overcome one of the massive hurdles that more people succumb to!

Final Thoughts

The two most common types of growth curves, exponential and logarithmic, can easily be applied to many areas of your life and the skills you are interested in investing time and energy into.

Try applying the lessons here to help you overcome the obstacles in your way. However, make sure you remember that all this knowledge means nothing if you aren’t willing to apply it.

More Tips on Learning and Growth

Featured photo credit: Alissa De Leva via unsplash.com

Reference

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Mark Lynch

Featured Life-Balance, & Personal Development Author

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Last Updated on May 13, 2020

9 Free Language Learning Apps That Are Fun to Use

9 Free Language Learning Apps That Are Fun to Use

Language learning apps are not only useful but also incredibly entertaining and fun. With our current ability to use language tools on the go, this is the golden age of language apps.

While they won’t replace real human interactions, language learning apps are an invaluable resource for learning the basics of a new language or for translating words in real-time.

There are hundreds of language learning apps being launched on a weekly basis, and it can be confusing to differentiate what’s useful from what’s not.

To help you save time, I’ve curated 9 free language learning apps that you should try and experiment with on your own.

1. Duolingo

    Duolingo is one of the most popular language tools out there. It’s perfect for beginners looking to dip their feet into learning a new foreign language. The site’s gamified approach to learning makes it fun to learn vocabulary, grammar, and basic words.

    Get the app here!

    2. Busuu

      Busuu offers a similar language learning experience in which you mix speaking, listening, writing, and reading activities. This helps you acquire a basic understanding of your target language.

      Get the app here!

      3. Babbel

        Babbel is an inexpensive and fun tool that uses algorithms to personalize your language learning experience. It is voiced by native speakers so you’ll also learn the proper pronunciations of words much easier.

        Get the app here!

        4. Ankiweb

          Anki has been around for a while, and its design is unique compared to other free language learning apps. It’s an electronic flashcard tool that makes it easy for you to remember phrases and words in a foreign language.

          Get the app here!

          5. Memrise

            Memrise is one of the leading platforms for memorizing anything. It’s mainly focused on language learning, but you can also use it to memorize words from certain fields and disciplines. You can use it to memorize vocabulary for your SAT exam, biology exam, etc.

            Get the app here!

            6. Tinycards

              Tinycards is an application launched by Duolingo. It’s a free and fun flashcard app that you can take on the go. You can choose from thousands of topics that have been created for you or create your own decks.

              Get the app here!

              7. Quizlet

                Quizlet is another free language learning app that offers more than learning language. It features free quizzes that help you learn just about anything. “Flashcards” is one of their most popular features, but you can also take tests, play games, or create your own quizzes to share with friends.

                Get the app here!

                8. Rype

                rype

                  Rype is a monthly membership site that connects you with fully-vetted professional language teachers for 1/10th of the price of a leading language school. Lessons are as short as 30 minutes, and you can schedule them at any time of the day, and any day of the week. For anyone with the desire to speak a foreign language fluently, Rype is worth checking out.

                  Get the app here!

                  9. Mindsnacks

                    Mindsnacks is another useful but also entertaining free language learning app. It offers fun brain games that you can play to activate your mind while also learning a foreign language. That’s hitting two birds with one stone!

                    Get the app here!

                    Final Thoughts

                    Learning another language gets harder as we age, but this shouldn’t stop us from trying. In fact, it’s much easier now to learn a new language because of the abundance of resources in our time.

                    So, check these apps out and try them for yourself!

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                    Featured photo credit: Debby Ledet via unsplash.com

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