Math

QuestionApproximate the average rate of change of infections from 0 to 8 days after April 1, 2020, using P(8)5.55P(8) \approx 5.55.

Studdy Solution

STEP 1

Assumptions1. The population infected on the8th day is5.55 thousand people. The population infected on the16th day is10.28 thousand people3. We are asked to find the average rate of change from0 to8 days

STEP 2

The average rate of change is calculated as the change in the dependent variable (in this case, the population infected) divided by the change in the independent variable (in this case, time). This can be written asAveragerateofchange=(t2)(t1)t2t1Average\, rate\, of\, change = \frac{(t2) -(t1)}{t2 - t1}

STEP 3

Now, plug in the given values for the population at time t1t1 (0 days) and t2t2 (8 days) to calculate the average rate of change.
Averagerateofchange=(8)(0)80Average\, rate\, of\, change = \frac{(8) -(0)}{8 -0}

STEP 4

Since the population at0 days is not given, we assume it to be0. Therefore, the equation becomesAveragerateofchange=(8)(0)8=.5508Average\, rate\, of\, change = \frac{(8) -(0)}{8} = \frac{.55 -0}{8}

STEP 5

Calculate the average rate of change.
Averagerateofchange=5.558Average\, rate\, of\, change = \frac{5.55}{8}

STEP 6

Round the answer to two decimal places.
Averagerateofchange=0.69Average\, rate\, of\, change =0.69So, the average rate of change of the number of infected people from0 to8 days is approximately0.69 thousand people per day.

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