The annual of Amazon.com from approximately $10.7 billion in 2006 to $34.2 billi

Question

The annual of Amazon.com from approximately $10.7 billion in 2006 to $34.2 billion in 2010. (a) Use this information to find both a linear model and an exponential model for Amazon. com's annual revenue I (in billions of dollars) as a function of time t in years since 2000. linear model I(t) = exponential model I(t) = Which of these models would you judge to be more appropriate to the data shown below? The is more appropriate. (b) Use the better of the two models from part (a) to predict the 2008 figure and compare it with the actual figure above. The model yields an estimate of $ billion, which is not too far from the actual figure.

Explanation / Answer

a)

Linear model

I=at+b

using first condition of 2006

10.7=6a+b ----------------------(1)

using 2nd condition of 2007

14.8=7a+b ------------------------(2)

solving equation 1 and 2 we get

a=4.1 and b=-13.9

I(t)=4.1 t - 13.9

exponential model

I=aebt taking ln on both side

ln I = ln (a) + bt

now

ln (10.7)= ln (a) + 6 b

and

ln (14.8)=ln (a) + 7 b

solving above 2 equation

ln a = 0.424 a=1.528 and b= 0.324

thus I(t)=1.528e0.324t

b)

using linear model

I(8)=4.1*8-13.9=18.9

using exponential model

I(8)=1.528e0.324*8=20.41

Hence better model is linear which give predicted population is 18.9 (billions)

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