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 [tex]{}[/tex] 0 [tex]{}[/tex] 10 [tex]{}[/tex] 10 [tex]{}[/tex] 10 [tex]{}[/tex] 10
16 [tex]{}[/tex] 1 [tex]{}[/tex] 16.07021 16.27604 16.34583 [tex]{}[/tex] 16.38095
26 [tex]{}[/tex] 2 [tex]{}[/tex] 25.43466 26.2797 26.574 26.72363
42 [tex]{}[/tex] 3 [tex]{}[/tex] 39.33834 41.89929 42.82868 43.30901
66 [tex]{}[/tex] 4 [tex]{}[/tex] 58.85058 65.51853 68.09014 69.45316
100 [tex]{}[/tex] 5 [tex]{}[/tex] 84.17395 99.55866 106.0177 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.
