Polynomial and Ln Y= Ln Essay

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PART A: 1. The equation of the trend line is y = 1.9496x0.5394 2. Substitute x=4, y=1.9496(4)0.5394, y= 4.06 seconds
PART C
b) The exponential model worked best for my recorded data because the dots fitted the linear line better.
c) The equation of the trend line is y = 60e-0.013x
5.
Half the value is 30cm. x=30, y= 60e -0.013x(30) 40.6 seconds. It will take 40.6 seconds to reach 30 cm.
6.
Relating the solution to the problem: In an exponential situation the value of the dependant variable will change by the same proportion over equal time periods. This can be seen by studying the concept of a half life. This is the time a dependant variable of an exponential function taken to reduce by half. State the problem: The problem in this simulation was to estimate the half life of the pendulum. My model of y= 60e-0.013x gave a half life of 40.6. | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |

Theory behind the model- The equation for an exponential model is y=aekx. The most common to fit a straight line to some data is linear regression. When we have a non-linear data, it is necessary to transform the data using logs so that it appears straight. Then linear regression can be used to find the parameters of the equation of the model. Mathematical proof to show the relationship between

y=aekx and y=mx+c.
Y=aekx
In y=(aekx)
In y = a + ekx
Ln y= ln a + kx ln e
Ln y = ln a +kx
Ln= kx + ln a

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