Archive for the ‘Exponential Functions’ Category
February 20, 2024
You have 2 parents, 4 grandparents, 8 great grandparents, ETC, ETC
The no. of ancestors you have per generation follows an EXPONENTIAL FUNCTION:
Here are the numbers going back 50 generations or 1,000 years.
When you plot YOUR NO. ANCESTORS over a POPULATION OF THE WORLD GRAPH there is a problem.
Population of the World DATA HERE
If you look at the graph (above) you will see that the No. YOUR ANCESTORS equalled the POPULATION OF THE WORLD about 500 years or 25 Generations ago.
You are related to everyone who was alive 500 years ago. Some of your ancestors inlcude:
Of course, EVERYONE else has these ancestors too.
If you go back 50 generations you have more ANCESTORS than the entire POPULATION OF THE WORLD.
Why?
Anthropologists say that there was a lot of IN BREEDING especially when humans lived in small tribes and the world population was small.
So way back every one of our family trees has members popping up all over the place. So we had far fewer ancestors than the math suggests.
Posted in Exponential Functions, Middle School, Real Life Math | Tagged ancestor, curve, equation, exponential, generations, Graph, Maths, Middle school, no. of ancestors, population, Problem, real life, Shakespeare | Leave a Comment »
November 13, 2021
I Can’t Sleep Math: Caffeine Maths METRIC HERE.
Sensitivity to caffeine varies for individuals, but in healthy adults the half life for caffeine is approx 6hrs meaning your body eliminates half the caffeine you have drunk in 6 hrs. Ref: Caffeine Pharmacology
Caffeine interferes with sleep. One study found that consuming caffeine 6 hours before bedtime reduced total sleep time by 1 hour.
Caffeine content sources Caffeine Content Data Base
Street art by JEKS, South Carolina
The Half life equation is an exponential function.
The Mayo Clinic advises up to 400mg Caffeine a day for adults, which would be;
10 black teas
7 instant coffees
4 cappuccinos
2 dark roast brewed
less than one cup of Black Insomnia Coffee.
Approx half this amount of caffeine for 14 yos.
Posted in Caffeine Math, Decimals, Exponential Functions, graphs, Senior School, units weight, Year 12 mathspig | Tagged back to school, caffeine, coffee, cups, de[rivation, equation, exponential, function, Graph, intake, levels, Math %, recommened, sleep, tea | Leave a Comment »
November 13, 2021
I Can’t Sleep: Caffeine Math USA UNITS HERE.
Sensitivity to caffeine varies for individuals, but in healthy adults the half life for caffeine is approx 6hrs meaning your body eliminates half the caffeine you have drunk in 6 hrs. Ref: Caffeine Pharmacology
Caffeine interferes with sleep. One study found that consuming caffeine 6 hours before bedtime reduced total sleep time by 1 hour.
Caffeine content sources Caffeine Content Data Base
Street art by JEKS, South Carolina
The Half life equation is an exponential function.
The Mayo Clinic advises up to 400mg Caffeine a day for adults, which would be;
9 black teas
6 instant coffees
4 cappuccinos
2 dark roast brewed
less than one cup of Black Insomnia Coffee.
Approx half this amount of caffeine for 14 yos.
Posted in Caffeine Math, Exponential Functions, graphs, Year 12 mathspig | Tagged back to school, caffeine, coffee, cups, de[rivation, equation, exponential, function, Graph, intake, levels, Math %, recommened, sleep, tea | Leave a Comment »
March 6, 2019
You will find TWILIGHT TV series Math here.
Posted in algebra, Exponential Functions, Hollywood Maths, Middle School, Senior School, TV SHOW Maths, Vampire Maths | Tagged algebra, challenge, exponential, function, horror, Math, Maths, Middle school, scary, simple, story, TV, Twilight, vampire | 2 Comments »
August 14, 2018
I Can’t Sleep Math: Caffeine Maths METRIC HERE.
Sensitivity to caffeine varies for individuals, but in healthy adults the half life for caffeine is approx 6hrs meaning your body eliminates half the caffeine you have drunk in 6 hrs. Ref: Caffeine Pharmacology
Caffeine interferes with sleep. One study found that consuming caffeine 6 hours before bedtime reduced total sleep time by 1 hour.
Caffeine content sources Caffeine Content Data Base
Street art by JEKS, South Carolina
The Half life equation is an exponential function.
The Mayo Clinic advises up to 400mg Caffeine a day for adults, which would be;
10 black teas
7 instant coffees
4 cappuccinos
2 dark roast brewed
less than one cup of Black Insomnia Coffee.
Approx half this amount of caffeine for 14 yos.
Posted in Caffeine Math, Decimals, Exponential Functions, graphs, Senior School, units weight, Year 12 mathspig | Tagged back to school, caffeine, coffee, cups, de[rivation, equation, exponential, function, Graph, intake, levels, Math, recommened, sleep, tea | 3 Comments »
August 14, 2018
I Can’t Sleep: Caffeine Math USA UNITS HERE.
Sensitivity to caffeine varies for individuals, but in healthy adults the half life for caffeine is approx 6hrs meaning your body eliminates half the caffeine you have drunk in 6 hrs. Ref: Caffeine Pharmacology
Caffeine interferes with sleep. One study found that consuming caffeine 6 hours before bedtime reduced total sleep time by 1 hour.
Caffeine content sources Caffeine Content Data Base
Street art by JEKS, South Carolina
The Half life equation is an exponential function.
The Mayo Clinic advises up to 400mg Caffeine a day for adults, which would be;
9 black teas
6 instant coffees
4 cappuccinos
2 dark roast brewed
less than one cup of Black Insomnia Coffee.
Approx half this amount of caffeine for 14 yos.
Posted in Caffeine Math, Exponential Functions, graphs, Year 12 mathspig | Tagged back to school, caffeine, coffee, cups, de[rivation, equation, exponential, function, Graph, intake, levels, Math, recommened, sleep, tea | 2 Comments »
July 10, 2015
Hellooooo My Little Sweeties,
There is so much maths you can do with m&ms, it’s hard to believe there is any other sort of maths.
You can study:
Counting, times tables, set theory, Bar graphs, Fractions, % and decimals, Mean, median, mode, and parabolas (using a really cool peg-powered catapult).
But my favouritest ,developed by Patrick Len, is using m&ms to demonstrate half life in radioactive substances and therefore write an exponential equation.
m+m ACTIVITY:
Throw a fixed no. m&ms on a table. Mathspig chose 128 m&ms for a very good reason. Eat the ones with the m showing. Count remainder. Throw again. Eat the ones with the m showing. Count remained. Keep doing this. You will end up with results like the following. (Not identical as chance is involved)
Wow! m&m’s and exponential equations. How yummy is that!!!!!!
More yummy maths:
m+m maths 1: find the volume using m+ms!
m+m maths 2: Guess, NO, calculate the number of m+ms in a jar!
m+m maths 3: how many m+ms will kill you?
m+m maths 4: How many m+ms will kill my dog?
m+m maths 5: how many m+ms will kill my cat?
m+m maths 6: How many m+ms will kill my pet rat?
m+ms maths 7: how many m+ms will kill my pet mouse?
Mmmmmmm! Can’t talk. Face full of chocolate.
Bye bye
Mathspig
Posted in %, 7 m+m maths challenges, algebra, Arithmetic, Averages, base 2, decimals, Exponential Functions, Middle School, Parabolas, Units Volume, units weight, Year 7 mathspig, Year 9 Mathspig | Tagged %, activity, algebra, back to school, bar graphs, exponential fn, fractions, Fun, m&m, Math %, mean, median, project, radioactive half life, volume | 1 Comment »
November 15, 2013
Lindsay Lohan may not be seen as the pin-up girl for Maths.
Yet her character Cady in the Mean Girls TV Series, not only does ‘math’ in 12th grade, she joins the the maths geeks as a mathlete and adds the term ‘The Limit does not exist’ to pop culture.
Her teacher is Mrs Norbury (Tina Frey).
Here is the good:
………………………………………………………………………………………..
Here is the bad:
Do girls still do this? Pretend they are dumb to impress a boy?
FYI Aaron!!!!!!!!!
n factorial = n! = 1x2x3x4x5x6x7x8x9x10 ………………………
………………………………………………………………..
Here is the Whoa! This is real maths … on the tellie:
And here is the maths from openstudy that Cady did in her head while thinking about not calling people stupid or fat:
Posted in algebra, Exponential Functions, Inverse Functions, Middle School, Senior School, TV SHOW Maths, Year 12 mathspig | Tagged aaron, CAdy, Lindsay Lohan, mathlete, mathletics, Mean girl math, mean girl maths, Mean Girls, mean girls maths, Mrs Norbury, The limit does not exist, TV series, TV show, youtube | 1 Comment »
August 29, 2013
Here are some google glasses that actually look cool.
Here’s what Google Glasses can do.
Instead of using the Google Maps on your phone the Google Glasses put the map onto the glass lense so you can see where to go and where you are going. Theoretically.
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The Maths
Google Maps uses GPS or Global Positioning System satellites and simple maths of TRIANGULATION or, in the case of the 3D model, 3D TRILATERATION to accurately locate your position on earth.
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You will find excellent explanations of how GPS works at the Nova Scotia Dept of Education website and by Diana Cooksey
MSU GPS Laboratory website.
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Simple Explanation:
GPS satellites broadcast two signals which allows the GPS program in your phone or device to calculate your distance from the satellite. GPS needs data from 3 satellites to locate your position on earth.
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2D Model:
Let’s assume your phone can calculate how far you are from a radio tower.
Tower 1:
Your phone can calculate how far your are from the tower but you could be anywhere on the first circle.
……………………………………………………..
Tower 1& 2:
Your phone can calculate your distance from two towers and locate you at one of two points where the circles intersect.
……………………………………………………….
Tower 1, 2 & 3:
Now you phone can accurately find your position at the intersection of 3 circles.
………………………………………………………………………………………………………….
3D Model:
Your phone can calculate how far you are from a satellite.
……………………………………………………………
Satellite 1:
You could be anywhere on the first sphere.
……………………………………………………………
Satellite 1 & 2:
You could be anywhere at the intersection of the two spheres. These spheres intersect along a circle.
……………………………………………………………
Satellite 1, 2 & 3:
The 3rd sphere will cross that circle at 2 points. As one position is not on earth it can be discarded.
………………………………………………………………………………………………………….
Error Alert:
All measurements have an inbuilt uncertainty (scientists call it an error) because the accuracy of instruments is limited. Measuring across such long distances makes for significant errors. One problem for GPS is signal interference.
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New Techno Frontiers in the Maths Classroom
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1. If you teach maths wearing Google glasses you can INSTANTLY record students bad behaviour in class on your computer. Wow! Evidence. THE FORCE BE WITH YOU, Mathspiggies.
OR
2. You can record a maths lesson using Google Glasses. It is already happening, my Sweeties. Have a look at this.
Posted in 10 Totally Awesome Reasons Why You Should Do Maths, Exponential Functions, geometry, Junior School, Middle School, Senior School, Year 12 mathspig, Year 7 mathspig, Year 9 Mathspig | Tagged 10 Amazing reasons why you should do maths, amazing, amazing maths, cool, Google Glasses, GPS, How GPS works, inspiring math, inspiring maths, Making Math Fun, Math %, math classroom, Math PR, Math promo, Maths, Maths Pr, Mr Google, Mr Google is Watching You, new technology, New technology in math, simple explanation, teaching maths with google glasses, Technology in math, technology in maths, The Force be with you, totally | 21 Comments »
August 6, 2013
If we double the rate of population growth in Australia, what will the population be in 38 years?
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Pop growth rate per year:…..r = 3.6 % = 0.036
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You can check your calculations here @ Wayne’s World Population Calculator.
Posted in %, Exponential Functions, Middle School, Rates, Senior School | Tagged Australia, Australian, controlling population, How long to double population, Middle School maths, Population growth, rate, World Population, World Population calculations | Leave a Comment »
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