Answer:
The function that models the scenario is given as follows;
[tex]P(t) = \dfrac{500}{1 + 49 \cdot e^{-0.5 \cdot t}}[/tex]
Step-by-step explanation:
The table of values are presented as follows;
The number of days, t, since the rumor started: 0, 1, 2, 3, 4, 5
The number of people, P, hearing the rumor: 10, 16, 26, 42, 66, 100
Imputing the given functions from the options into Microsoft Excel, and
[tex]A = P(t) = \dfrac{250}{1 + 24 \cdot e^{-0.5 \cdot t}}[/tex]
[tex]B = P(t) = \dfrac{500}{1 + 49 \cdot e^{-0.5 \cdot t}}[/tex]
[tex]C = P(t) = \dfrac{750}{1 + 74 \cdot e^{-0.5 \cdot t}}[/tex]
[tex]D = P(t) = \dfrac{1000}{1 + 99 \cdot e^{-0.5 \cdot t}}[/tex]
solving using the given values of the variable, t, we have;
P         t        A         B    [tex]{}[/tex]       C            D
10 Â Â Â Â [tex]{}[/tex] Â Â Â 0 Â Â Â Â [tex]{}[/tex] Â Â 10 Â Â Â Â [tex]{}[/tex] Â Â Â Â 10 Â Â Â Â [tex]{}[/tex] Â Â Â Â Â 10 Â Â Â Â [tex]{}[/tex] Â Â Â Â Â Â 10
16 Â Â Â Â [tex]{}[/tex] Â Â Â 1 Â Â Â Â [tex]{}[/tex] Â Â Â 16.07021 Â Â Â 16.27604 Â Â Â 16.34583 Â Â Â Â [tex]{}[/tex] 16.38095
26 Â Â Â Â [tex]{}[/tex] Â Â 2 Â Â Â Â [tex]{}[/tex] Â Â 25.43466 Â Â Â 26.2797 Â Â Â 26.574 Â Â Â Â Â Â 26.72363
42 Â Â Â Â [tex]{}[/tex] Â Â 3 Â Â Â Â [tex]{}[/tex] Â Â 39.33834 Â Â Â 41.89929 Â Â Â 42.82868 Â Â Â Â 43.30901
66 Â Â Â Â [tex]{}[/tex] Â Â 4 Â Â Â Â [tex]{}[/tex] Â Â 58.85058 Â Â Â 65.51853 Â Â Â 68.09014 Â Â Â Â 69.45316
100 Â Â Â Â [tex]{}[/tex] Â 5 Â Â Â Â [tex]{}[/tex] Â Â 84.17395 Â Â Â Â 99.55866 Â Â 106.0177 Â Â Â Â Â 109.5721
Therefore, by comparison, the function represented by [tex]B = P(t) = \dfrac{500}{1 + 49 \cdot e^{-0.5 \cdot t}}[/tex] most accurately models the scenario.
