Question

Review the table.

Answer 1

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.

Answer 2

Answer:

b

Step-by-step explanation: