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Exponential Modeling
In an earlier chapter, you learned about linear and quadratic modeling. Now you will be doing a few problems that involve exponential modeling.
Problem
The data below shows the average speed of a computer and the year
( 1976 = 0) it was made.
The speed of the computer was tested every 2 years.
~ A table was generated with the years (incremented by 2) and the speed in MHz.
~ Looking at this graph it is not linear, nor quadratic. It is an exponential graph.
~ Because this graph appears to be growing faster and faster as the years increase, we can see that is an Exponential Growth graph.
~ To determine the exponential growth model equation, we can use Desmos to generate it.
~ Generic equation: y1 ~ abx1
~ A graph for this data was generated using Desmos.
~ The x-axis represents the years.
~ The y-axis represents the speed (MHz)
~ The values have been generated by Desmos
a = 2.54436 and b = 1.20173 y = 2.54436 · 1.20173x
~ We can use these values to determine the speed of a computer in 1996 ( year: x = 20)
~ Desmos graphed a horizontal orange line intersecting the exponential graph at (20, 100.399),
~ This indicates that the processing speed of a computer in 1966 was 100.399 MHz.
~ Is this model valid? Today's processing speed of desktop computers run around 3-4 GHz.
Notice it is not MHz, but GHz. (MHz is one million cycles per second, and GHz is one billion cycles per second.)
~ The exponential model, y = 2.54436 • 1.20173x, can be used to predict the processing speed of future computers.
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