Question

The logistic model P(t) = 94.5148/ 1 + 0.0368e⁰.²³⁵²t represents the percentage of households that do not own a personal computer t years since 1986.

(a) Evaluate and interpret P(O). Evaluate P(O).
P(O)= __%
(Round to one decimal place as needed.)
Which sentence below best describes P(O)?
A. P(0) is the percentage of households without a personal computer in 1986.
B. P(0) is the year no households had a personal computer.
C. P(0) is the year all households had a personal computer.
D. P(0) is the percentage of households with a personal computer in 1986.

Answer 1

P(0) evaluates to approximately 91.2% and represents the percentage of households without a personal computer in the year 1986, which aligns with option A.

Step-by-step explanation:

The given logistic model is P(t) = 94.5148 / (1 + 0.0368e0.2352t), which represents the percentage of households that do not own a personal computer t years since 1986. Evaluating P(0), we substitute t with 0 in the equation:

P(0) = 94.5148 / (1 + 0.0368e0.2352×0) = 94.5148 / (1 + 0.0368e0) = 94.5148 / (1 + 0.0368) = 94.5148 / (1.0368) = 91.2%

Therefore, P(0) is approximately 91.2%. The correct interpretation of P(0) is that it represents the percentage of households without a personal computer in 1986, which corresponds to option A. It is not a year, nor does it represent households with a computer; therefore, options B, C, and D are not correct.