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Exponential Graphs

Exponential Graphs. Rafay , Ayesha, Tilak. Exponential Graphs. Growth:. Decay:. WHAT ARE EXPONENTIAL FUNCTIONS

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Exponential Graphs

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  1. Exponential Graphs Rafay, Ayesha, Tilak

  2. Exponential Graphs Growth: Decay: WHAT ARE EXPONENTIAL FUNCTIONS An exponential function is a graph that shows a growth and/or decay of a quantity by a fixed amount (value/percent) at regular time periods. The basic equation for an exponential function is F(x) = abx. The ‘a’ value in the graph is the initial amount before the growth begins. The ‘b’ value is the growth rate. And the ‘x’ value is the time period. An exponential graph has either a Growth and/or Decay. The graph when the ‘a’ value is greater 0 and the ‘b’ value is between 0 and 1 the graph is decreasing (decaying). The graph when the ‘a’ value is greater 0 and the ‘b’ value is greater than 1 the graph is increasing (growth). If a table of value is representing a graph the ratios between each value tell us if the graph is exponential or not. If the ratios are equivalent than the graph is exponential, if not than the graph is not an exponential function. Exponential graphs are commonly used to show data that relates to the Past, Current, and Future real life situation.

  3. Cell Phone Users From 1986 - 1994 Real Life Example In 1985, there were 285 cell phone subscribers in the small town of Centerville, the number of subscribers increased by 75% per year after 1985. • Data: Number of Cell Phone users from 1986-1994 in Centerville • This is the data for the number of cell phone users in a specific time and location. It is not to old and not to recent but we can use this data to discuss real life trends and statistics.

  4. Cell Phone Users From 1986 - 1994 Data Graphed For The Number of Cell Phone Users From 1986 – 1994 Exponential Graph (Growth)

  5. Cell Phone Users From 1986 - 1994 Equation The equation for this graph would be: f(x)=285(1.75)x In this graph/equation:285 is the original value of when people actually started to use phones. And 1.75 is the growth rate of the number of phone users that increases every year. And the x value will be the number of years. We can use this equation to find out the number of cell phone users in the future or to find trends that may lead to the growth or decay of this exponential function. Restrictions D={x∈R|x >0} R={y∈R|285<y<43871} Reasoning This is an exponential Graph because the ratios of the data are consistence and increasing by a value of 1.75 per year from Year 1986 to Year 1994. This means that the graph has an exponential growth. You can also see this in the graph that over time that the number of cell phone users are increasing. There are not outliers or any points on the graph which show or indicate that the number of cell phone users ever dropped or are going to drop. We can say that if this graph continued it would probably not decrease or change its consistency.

  6. Real World Application This graph relates to real life because this is a graph that has data from real world . We can use this to predict the future or past information regarding the number of cell phone users over years. Based upon our graph we predict that the graph will continue to increase because population will increase which will also increase the number of cell phone subscribers. We can compare this data to the whole USA population. And this can tell us the overall cell phone subscribers in USA. This would also include Centerville.

  7. Cell Phone Subscribers From 1985 – 2006 In USA

  8. Cell Phone Subscribers From 1985 – 2006 In USA Equation The equation for this graph would be: f(x)=248331(1.37)x In this graph/equation:248311 is the original value of when people actually started to use and subscribe for phones.And 1.37 is the growth rate of the number of phone user subscribers that increases every year. And the x value will be the number of years. We can use this equation to find out the number of cell phone users in the future or to find trends that may lead to the growth or decay of this exponential function. Restrictions For this Graph with current data the restrictions will be: D={x∈R|x >0} R={y∈R|248331<y<233000000} Reasoning This is an exponential Graph because the ratios of the data are consistence and increasing by a value of 1.37 per year or 37% from Year 1986 to Year 1994. This means that the graph has an exponential growth. You can also see this in the graph that over time that the number of cell phone subscribers are increasing. There are not outliers or any points on the graph which show or indicate that the number of cell phone users never dropped. We can say that if this graph continued it would probably not decrease or change its consistency.

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