In 2020, the world was exposed to a novel coronavirus called Covid-19. The virus resulted in a pandemic throughout many countries. In the United States, the number of individuals infected with Covid-19 grew rapidly in the early stages of the disease reaching the country. The data below represent the cumulative number of documented cases of Covid-19 in 2020 during the early phase of the disease. Let x represent the number of days since February 20, 2020.

(a) Draw a scatter plot treating days since February 20 as the independent variable.

(b) Using a graphing utility, build an exponential model from the data.

(c) Express the function found in part (b) in the form N(t) = N₀e^kt.

(d) Graph the exponential function found in part (b) or (c) on the scatter plot.

(e) Use the exponential function from part (b) or (c) to predict the cumulative number of cases of Covid-19 on April 5 (x = 45).

(f) Use the exponential function from part (b) or (c) to predict when the cumulative number of cases reached 1,000,000.

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Date Feb 20 (x0) Feb 25 (x = 5) March 1 (x = 10) March 6 (x = 15) March 11 (x = 20) March 16 (x = 25) March 21 (x 30) March 26 (x = 35) March 31 (x = 40) Cumulative Number of Cases 15 57 75 319 1301 4596 24,192 85,435 188,530