In Russia the average consumer drank two servings of Coca-Cola in 1993. This amount appeared to be increasing exponentially with a doubling time of 2 years. Given a long-range market saturation estimate of 100 servings per year, find a logistic model for the consumption of Coca-Cola in Russia and use your model to predict when, to the nearest year, the average consumption will be 41 servings per year.
A)Sometime in 1993.
B)Sometime in 2003.0.
C)Sometime in 2004.
D)Sometime in 2005.
E)Sometime in 2003.

Question

Quizplus · Accepted Answer

The doubling time is 2 years, so the growth rate is k=ln(2)/2=0.3466. The carrying capacity is L=100. The logistic model is P(t)=L/(1+Ce^(-kt)), where C is a constant. We have P(0)=2, so 2=100/(1+C), which gives C=49. Therefore, the logistic model is P(t)=100/(1+49e^(-0.3466t)). To find when the average consumption will be 41 servings per year, we solve the equation 41=100/(1+49e^(-0.3466t)) for t. We get t=ln(100/41-1)/(-0.3466)=10.005. Therefore, the average consumption will be 41 servings per year sometime in 2003.

In Russia the Average Consumer Drank Two Servings of Coca-Cola