Question

The logistic model P(t) = (1 + 0.0418e^(-0.24521t))^(-1) represents the percentage of households that do not own a personal computer t years since 1985. Evaluate and interpret P(0). Evaluate P(0).

Answer 1

To evaluate P(0), substitute t with 0 in the logistic model P(t) = (1 + 0.0418e^{-0.24521t})^{-1}. After simplification, P(0) ≈ 0.9597 or 95.97%, representing the estimated percentage of households without a personal computer in 1985.

Step-by-step explanation:

The logistic model P(t) = (1 + 0.0418e^{-0.24521t})^{-1} represents the percentage of households that do not own a personal computer t years since 1985. To evaluate P(0), we would substitute t with 0 in the model and simplify.

Evaluate P(0):

• Substitute t with 0: P(0) = (1 + 0.0418e^{-0.24521(0)})^{-1}
• Simplify the exponent: P(0) = (1 + 0.0418e^0)^{-1} since e^0 = 1
• Calculate the addition: P(0) = (1 + 0.0418)^{-1}
• Finish the calculation: P(0) = 1/(1 + 0.0418) ≈ 1/1.0418 ≈ 0.9597 or 95.97%

The interpretation of P(0) ≈ 95.97% is that approximately 95.97% of households did not own a personal computer in the year 1985 when this logistic model's timeline starts.