Compact florescent light bulbs save energy when compared to traditional incandes

Question

Compact florescent light bulbs save energy when compared to traditional incandescent bulbs. Our green energy campaign includes efforts to get local residents to change their incandescent bulbs to florescent bulbs. Initially 192 households make the change. Market studies suggest that, in the absence of limiting factors, we could increase that number by 26% each month. In our target area, there are 259,392 households, which we take as the limiting value. Make a logistic model that gives the number of households converting to florescent bulbs after t months. (Use t as your variable. Round r to three decimal places.) N(t) =

Explanation / Answer

Initially 192 households make the change from traditional incandescent bulbs to compact florescent light bulbs. After 1 month, the number of the households who have made the change increases to 192+0.26*192. After 2 months, the number of the households who have made the change, increases further to 192+ 0.26*(192+0.26*192) = 192+0.26*192+(0.26)2*192. Thus, after t months, the number of the households who have made the change is given by N(t) = 192+0.26*192+(0.26)2*192+…+(0.26)t*192 = 192[1+0.26+(0.26)2+…+(0.26)t] = 192[1-(0.26)t+1]/(1-0.26) = (192/0.74) [1-(0.26)t+1] = (9600/37)[1-(0.26)t+1]

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