3. (6 pt) 1(i) Here is some recent data on recent COVID (found on the US Center for Disease Control's website https://data.cdc.gov/Case-Surveillance/United-States-COVID-19-Cases-and-Deaths-by-State-o/9mfq-cb36/data). We have rounded:
Data Point
Date
Weeks t passed since 10.18.20
# of new Confirmed Covid Cases C(t) this day (thousands)
Data Point as an ordered pair( , )
A
10.18.20
79.4
B
10.25.20
88.5
Let us assume that cases grow at an exponential rate, with daily cases given by the formula (**): C(t) = Q0 * e^(kt), where t is weeks passed since 10.18.20.
(i) Make your own chart and fill in the empty cells.
(ii) Let's review your Math 129 a bit: Write two equations based on (**), one for A, another for B.
(iii) Solve simultaneously for Q0 and for k. Write your k to three decimal places. Be sure to show all of your algebra steps.
(iv) Use (iii) to write the equation for thousands of cases predicted for week t.
(v) Draw a rough sketch of function (**). Be sure to label both axes with their units, and label points A and B with their coordinates.
(vi) How many new cases does the model in (iv) predict there will be on 11.01.20?
(vii) Now draw the tangent line at B.
(vii) Find the instantaneous growth rate of new cases per day per week on 10.25.20, based on your model (iv). Answer in a complete sentence, and then write the equation of this tangent line.
(viii) How many new cases would the tangent line predict there will be on 11.01.20?
(ix) How many new cases does the model in (iv) predict there will be on 11.01.20?
(x) Finally, go to the website and find the actual number of new confirmed cases reported on 11.01.20.
(xi) In a brief paragraph, summarize your findings from (viii), (ix), and (x). Be sure the verb "UNDERESTIMATE" appears at least once in your paragraph.