# Write an exponential function showing the relationship between y and t

High School Statutory Authority: Algebra I, Adopted One Credit. Students shall be awarded one credit for successful completion of this course. This course is recommended for students in Grade 8 or 9. What does it really mean? Math books and even my beloved Wikipedia describe e using obtuse jargon: The mathematical constant e is the base of the natural logarithm. And when you look up the natural logarithm you get: The natural logarithm, formerly known as the hyperbolic logarithm, is the logarithm to the base e, where e is an irrational constant approximately equal to 2.

Nice circular reference there. Save your rigorous math book for another time. Pi is the ratio between circumference and diameter shared by all circles.

It is a fundamental ratio inherent in all circles and therefore impacts any calculation of circumference, area, volume, and surface area for circles, spheres, cylinders, and so on.

Pi is important and shows all circles are related, not to mention the trigonometric functions derived from circles sin, cos, tan. Just like every number can be considered a scaled version of 1 the base unitevery circle can be considered a scaled version of the unit circle radius 1and every rate of growth can be considered a scaled version of e unit growth, perfectly compounded.

So e is not an obscure, seemingly random number. And it looks like this: Splitting in two or doubling is a very common progression. Sure, we can triple or quadruple, but doubling is convenient, so hang with me here.

Mathematically, if we have x splits then we get 2x times as much stuff than when we started. With 1 split we have 21 or 2 times as much. As a general formula: We can rewrite our formula like this: So the general formula for x periods of return is: A Closer Look Our formula assumes growth happens in discrete steps.

Our bacteria are waiting, waiting, and then boom, they double at the very last minute. Our interest earnings magically appear at the 1 year mark. Based on the formula above, growth is punctuated and happens instantly. The green dots suddenly appear.

If we zoom in, we see that our bacterial friends split over time: After 1 unit of time 24 hours in our caseMr. He then becomes a mature blue cell and can create new green cells of his own.

Does this information change our equation?

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The equation still holds. Money Changes Everything But money is different.For those primarily interested in the changes since version , the appendix Changes since version (§I) is the recommended starting point.

An accompanying version of this document displays in color all changes to normative text since version ; another shows changes since the previous Working Draft. Let t be the number of hours since the start of the study. Let y be the number of bacteria cells Write an exponential function showing the relationship between y and t.

Let t be the number of years since the start of the study. Let y be the area that the forest covers in km2 Write an exponential function showing the relationship between y and t. Let t be the number of years since the start of the study. Let y be the area that the forest covers in barnweddingvt.com an exponential function showing the relationship between y and t.

SCHEME OF WORK / 1 September / 13 comments. PRESENTATION NATIONAL HIGH SCHOOL, BENIN CITY.