The function p(w)= 230(1.1)^w represents the number of specialty items produced at the old factory w weeks after a change in management. the graph represents the number of specialty items produced at the new factory during the same period.

From the given graph  (a) during week 0, how many more specialty items were produced at the old factory than at the new factory? explainfrom the function: p(w)= 230(1.1)^wthe number of specialty produced in the old factory will be: p(w)=p(0)= 230(1.1)^0p(0)=230(1)p(0)=230number of specialty produced in the new factory: p(0)=190the difference in the production was: 230-190=40 specialty(b) find and compare the growth rates in the weekly number of specialty items produced at each factory. show your workthe growth rate of old factory from the function: p(w)= 230(1.1)^wgrowth rate=1.1-1=0.1~10%growth rate of the new factory is: taking 2 consecutive points: (0,190) and (1,220)the rate of growth is: (220/190)-1=0.158~15.8%thus we conclude that the new factory has a higher growth rate as compared to the old factory.(c) when does the weekly number of specialty items produced at the new factory exceed the weekly number of specialty items produced at the old factory? explainthe model of the new factory is given by exponential model: y=ab^xwhere: a=initial valueb=growth ratex=w=timeplugging the values we obtain: y=190(1.16)^wthe point at which production in new factory will be more that old factory will be: 190(1.16)^w> 230(1.1)^wsolving for w  w=3.59376w~4thus the answer is after 4 weeks

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