EXPONENTIAL FUNCTION
What is an Exponential Function.Before we dive into what an exponential function is, what is an exponent? An exponent basically means power, for example, in 6^8 (^ means to the power of), the number 8 is the exponent, the number 6 is the base. In an exponential function, for example, y=2^x, x, the variable, must be the exponent. But there are other rules. The base, in this case, 2, must
1. Be a positive number 2. Not be the number 1 Repeat 1. Not be a negative number 2. Not be the number 1 Do you remember? Everyone shout! Don't you dare lie, we can find out. Who determined the Function
Procedure for Graphing the Function on Excel (Manually go through the steps)How to graph an Exponential FunctionProperties |
Where is it used in the real world?Exponential Functions are used in a variety of different areas like;
Uses for the functionThe exponential function is used because it is useful to calculate the population in a city for years to come in realistic terms, as more people having more babies means a quicker growth. This is useful as it shows how much a city will need to adapt over the coming years, meaning infrastructure will not go to waste. It also means that the government does not waste unnecessary taxpayer money. It is also used to predict the outcome of an investment in the coming weeks, months or years. Another use is to predict the decaying of a radioactive substance. this can be useful in cases like Chernobyl and Fukushima where scientists need to find out when a chemical will become safe enough to touch and for people to live there.
How is it used in the real world?A good example would be POPULATION
For example, in the town of China, the population is 10 000 000 000 in 2003, with the growth of 9.9% annually. That means after one year the population would be 10 000 000 000 + 0.099(10 000 000 000) The growth factor is 1.099 In the equation y=ab^x (^ means to the power of) y is the population you are trying to find a is the initial amount of people (which in this case is 10 000 000 000) b is the growth or decay factor, in our scenario it would be growth of population The exponent (x) is the amount of time, so for us that would be 2003 to now (12 years) to find the value of ‘y’, we would do ; 10 000 000 000(1.099)^12 Examples of Exponential FunctionsAn Exponential Function could either be an exponential growth or exponential decay. For an exponential growth, the base must be higher than 1. For a decay, the base must be lower than one, but not lower than 0 otherwise it won't be an exponential function at all!
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Have you been paying attention? Let's find out with a few questions!
First, are these exponential functions or not?
First, are these exponential functions or not?
ANSWERS! (OI IF UR NOT DONE GO BACK UP, NOTHING TO SEE HERE)
Q1: Is y=x^2 an exponential function?
Answer: As much as i love it being a function, it is unfortunately not an exponential function, since there is no x in the exponent
Q2: Is y=-2^x an exponential function?
Answer: This time, x is the exponent, which is amazing, but the base (-2), must not be a negative number.
Q3. Is y=1^x an exponential function?
Answer: Well, this time, the base (1) is a positive number. But, we said the base cannot be 1 either!
If you got any of the previous 2 questions right, YOU LIED!!! WE SAID WE COULD FIND OUT! WHY???
Q4. Is y=0.5^x an exponential function?
Answer: This time, the base is a positive number. But have you forgotten the last rule for a exponential function? Jokes, there isn't one, so the answer is yes, y=0.5^x is an exponential function
Answer: As much as i love it being a function, it is unfortunately not an exponential function, since there is no x in the exponent
Q2: Is y=-2^x an exponential function?
Answer: This time, x is the exponent, which is amazing, but the base (-2), must not be a negative number.
Q3. Is y=1^x an exponential function?
Answer: Well, this time, the base (1) is a positive number. But, we said the base cannot be 1 either!
If you got any of the previous 2 questions right, YOU LIED!!! WE SAID WE COULD FIND OUT! WHY???
Q4. Is y=0.5^x an exponential function?
Answer: This time, the base is a positive number. But have you forgotten the last rule for a exponential function? Jokes, there isn't one, so the answer is yes, y=0.5^x is an exponential function