QuestionApproximate the average rate of change of infections from 0 to 8 days after April 1, 2020, using $P(8) - P(0)$ .

Studdy Solution

STEP 1

Assumptions1. The number of infected people8 days after April1,2020 is5.55 thousand people. . The number of infected people16 days after April1,2020 is10.28 thousand people.
3. We are asked to find the average rate of change over the time interval from0 days to8 days.

STEP 2

The average rate of change is given by the formula $Average\, rate\, of\, change = \frac{Change\, in\, y}{Change\, in\, x}$ where $y$ represents the number of infected people (in thousands) and $x$ represents the time (in days).

STEP 3

For the time interval from0 days to8 days, the change in $y$ (number of infected people) is the number of infected people on the8th day minus the number of infected people on the0th day. Since the graph starts from0, the number of infected people on the0th day is0. So, the change in $y$ is $Change\, in\, y = y_{8\, days} - y_{0\, days} =5.55 -0 =5.55$

STEP 4

The change in $x$ (time) for the interval from0 days to8 days is $Change\, in\, x = x_{8\, days} - x_{0\, days} =8 -0 =8$

STEP 5

Now, we can calculate the average rate of change over the time interval from0 days to8 days by substituting the values of $Change\, in\, y$ and $Change\, in\, x$ into the formula $Average\, rate\, of\, change = \frac{Change\, in\, y}{Change\, in\, x} = \frac{5.55}{8}$

STEP 6

Calculate the average rate of change.
$Average\, rate\, of\, change = \frac{5.55}{8} =0.69$ So, the average rate of change of the number of infected people in Minnesota from0 days to8 days after April1,2020 is approximately0.69 thousand people per day.

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