Logistic Model for Household Conversions to Fluorescent Bulbs
How can we predict the number of households converting to fluorescent bulbs using a logistic model?
With the given data, how do we determine the constant B for the logistic model?
Answer:
A logistic model can be used to predict the number of households converting to fluorescent bulbs after t months. The formula for the model is N(t) = K / (1 + A * e^(-B*t)), where N(t) represents the number of households, K is the limiting value (239,408 in this case), A is the initial growth rate (0.21), and B is a constant.
A logistic model is commonly used to model population growth, where the growth rate decreases over time as the population reaches its limiting value. In this case, the limiting value is the total number of households in the target area, which is 239,408. The initial growth rate, A, is given as 0.21, which means that the number of households converting to fluorescent bulbs is expected to increase by 21% each month.
The constant B is determined using the initial data, where 208 households initially make the change. By solving the equation, we find that B is approximately 3.327. With this logistic model, we can predict the number of households converting to fluorescent bulbs after t months by plugging in the value of t into the formula N(t) = 239,408 / (1 + 0.21 * e^(-3.327*t)).