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The relationship between a sound's intensity and how it changes with distance is defined by the inverse square law:. Where I represents the sounds intensity in decibels at locations 1 and 2 and D represents distances 1 and 2 from the source of the sound. I live in subdivision where the houses are approximately 20ft apart. My old cat loved to sit on the fence between my house and my neighbor's house. Therefore, the distance from his position and my neighbor's open window is roughly 10ft. Let's assume that my neighbor's ear is about 5 additional feet away from the window.

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So for this example, a cat's yowl that has an intensity of 45 decibels at only 6 inches away would register In fact, according to my research, it usually takes sounds louder than 45 decibels to wake someone up from a deep sleep. Well, I guess one cat isn't enough to wake the neighbors, so we will need to do a few more calculations to determine how many cat's we need. First, lets back calculate and determine how loud of a noise is needed at the fence to wake the neighbor who is sleeping soundly just 20ft away.

To get a sound of 45 decibels at my neighbor's ear, we would need something that yells at just over 75 decibels near the fence. So 75 decibels is our target noise level. Below is an equation that can be used to add multiple sound sources together to compute the resultant sound level. This equation assumes that all of the sound sources produce the same intensity of noise.

Where L T is the total sound intensity decibels , L o is the sound intensity decibels for one source, and n is the number of sound sources. So for example, if one cat can produce 45 decibels, then 2 cats together can produce 48 decibels. To reach a sound intensity of 75 decibels, the equation reveals that approximately 1, cats would be needed to accomplish this feat. So perhaps if I wanted to wake my neighbors, it would be better to get a dog instead.

For fun, I've created neat graph showing the relationship between the number of cats meowing together in harmony and their total sound output in decibels. Armed with the information from my first cat mathematics article, the cats covering a standard American Football field could produce a sound as loud as It sure takes a lot of cats to make a loud sound. And that's the perfect segue into my next topic - Cat population growth.

With an average gestational period of about 66 days, the domestic cat gives birth to an average of 4 kittens per litter. Domestic cats also reach maturity at around 6 months old on average and have the ability to breed for about 10 years. Given this, I had two questions that I wanted answered: 1 Given the ability to grow unrestricted, how long would it take a group of 2 cats to turn into 1, cats, and 2 How many cats would there be after 10 years of reproduction?

The growth of any population, including cats, can be modeled using a simple exponential equation. Given the complex nature of population growth especially uncontrolled growth I've prepared a visualization to help us understand what is happening.


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The image below represents the growth pattern after 8 six month intervals starting with only 2 cats. As you can see, the pattern can get quite complex and after only 8 iterations representing 4 years , there are a total of cats. Now we can prepare an equation to calculate the population at an moment in time at least up until the cats start passing away.

Below is the general form of an exponential equation that represent an idealized population growth situation:. Where N represents the total population, N o is the initial population, r represents the growth rate, and t represents the time intervals.

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Using for N , 2 for N o , and 8 for t , we can quickly compute the growth rate which is 0. Now we have everything we need to answer my two questions. For the first question, I want to know how long it would take to reach cats. Therefore, t is computed to be 8. Since cats reproduce in 6 month intervals, we'll say that at 4. For the second question I wanted to know how many cats there would be after 10 years 20 six month intervals of growth. Therefore, N is computed to be an amazing 3,, cats!

This enough cats to fill almost standard forty-foot shipping containers! Next to arithmetic, geometry is probably one of the most practical applications for mathematics that you will ever learn.

Cat Population Growth

Geometry has all kinds of uses in construction, engineering, and surveying as well as design and manufacturing. Today, we can apply some simple geometry concepts to cats as well. Below is a picture of Circle Cat. This fluffy kitty is sleeping in a near perfect circle. From a previous article on the subject of cats and math, we discovered that the length of a typical American domestic cat from nose to tail is 2.


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    5. Assuming that the 2. Therefore r is equal to 4. The cool thing is that if anyone ever asks you what the radius of a cat is, you can confidently reply: "Why, it's about 5 inches sir, 4. No cats were harmed in the making of this article. The scenarios presented are not meant to resemble real life events and any similarities to such are purely coincidental. Sign in or sign up and post using a HubPages Network account. Comments are not for promoting your articles or other sites.

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    I love cats, they are so nice and friendly. If you're using my higher-level materials Geometry , Algebra II , Precalculus , Calculus without having gone through my Algebra I course , then I highly recommend that you read the cat-on-swing book.

    It will quickly bring you up-to-speed with all the math language ideas you need to fully benefit from my lessons. You'll learn that numbers have lots of different names, and math is the renaming tool. It's an easy read. If you can add, subtract, multiply and divide with numbers like 1, 2, and 3, then you can read this book.

    Supplement any math class, 7th grade through college. Use for self-learners, home-schoolers, math lovers, math haters. I found meat, potatoes, and pie on every page. It's all dessert. You rock!!!! Happy studying!

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