Question

The logistic model P(t)=(96.7436)/(1+0.0375e⁰.²²²⁶ᵗ represents the percentage of households that do not own a personal computer t years sinc 1985. Complete parts (a)-(d). (a) Evaluate and interpret P(0). Evaluate P(0). P(0)=% (Round to one decimal place as needed.)

Answer 1

To evaluate P(0), substitute t=0 into the logistic model. It shows that approximately 93.3% of households did not own a personal computer in 1985.

Step-by-step explanation:

To evaluate P(0), we will substitute t=0 into the logistic model given by P(t) = 96.7436 / (1 + 0.0375e0.2226t). The exponent will become 0.2226×0, which is 0, and since e to the power of 0 is 1, we have 0.0375e0 = 0.0375×1 = 0.0375. Thus, P(0) can be calculated as follows:

P(0) = 96.7436 / (1 + 0.0375) = 96.7436 / 1.0375 ≈ 93.3%

Interpreting P(0), this result indicates the percentage of households that did not own a personal computer in the base year of the model, which is 1985. Therefore, approximately 93.3% of households did not own a personal computer in 1985.