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3 years ago

Review the table.

Mathematics

2 answers:

Lynna [10]3 years ago

7 0

Answer:

The function that models the scenario is given as follows;

$P(t) = \dfrac{500}{1 + 49 \cdot e^{-0.5 \cdot t}}$

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

$A = P(t) = \dfrac{250}{1 + 24 \cdot e^{-0.5 \cdot t}}$

$B = P(t) = \dfrac{500}{1 + 49 \cdot e^{-0.5 \cdot t}}$

$C = P(t) = \dfrac{750}{1 + 74 \cdot e^{-0.5 \cdot t}}$

$D = P(t) = \dfrac{1000}{1 + 99 \cdot e^{-0.5 \cdot t}}$

solving using the given values of the variable, t, we have;

P t A B ${}$ C D

10 ${}$ 0 ${}$ 10 ${}$ 10 ${}$ 10 ${}$ 10

16 ${}$ 1 ${}$ 16.07021 16.27604 16.34583 ${}$ 16.38095

26 ${}$ 2 ${}$ 25.43466 26.2797 26.574 26.72363

42 ${}$ 3 ${}$ 39.33834 41.89929 42.82868 43.30901

66 ${}$ 4 ${}$ 58.85058 65.51853 68.09014 69.45316

100 ${}$ 5 ${}$ 84.17395 99.55866 106.0177 109.5721

Therefore, by comparison, the function represented by $B = P(t) = \dfrac{500}{1 + 49 \cdot e^{-0.5 \cdot t}}$ most accurately models the scenario.

Anika [276]3 years ago

5 0

Answer:

Step-by-step explanation:

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Answer with explanation:

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