(a) The number of cases on May 1, 2014, was approximately 188.59.
(b) The number of cases on November 24, 2014, was approximately 27107.76.
(c) C(92) = 1715.70.
This means that on the 92nd day from May 1, 2014, the number of Ebola cases in Africa was approximately 1715.70.
Computed using the exponential equation, [tex]C(t) = 188.59e^{0.024t}[/tex].
We are given that the spread of the Ebola virus in Africa in 2014 could be modeled by the exponential equation, [tex]C(t) = 188.59e^{0.024t}[/tex], where C represents the number of cases and t represents the number of days since May 1, 2014.
(a) In the question, we are asked for the approximate number of cases on May 1, 2014.
Since, the date is May 1, 2014, t = 0.
Thus, the number of cases, C, can be calculated by putting t = 0, in the exponential equation, [tex]C(t) = 188.59e^{0.024t}[/tex].
[tex]C(0) = 188.59e^{0.024*0}\\\Rightarrow C(0) = 188.59e^0\\\Rightarrow C(0) = 188.59[/tex]
Thus, the number of cases on May 1, 2014, was approximately 188.59.
(b) In the question, we are asked for the approximate number of cases on November 24, 2014.
Since, the date is November 24, 2014, t = 207.
Thus, the number of cases, C, can be calculated by putting t = 207, in the exponential equation, [tex]C(t) = 188.59e^{0.024t}[/tex].
[tex]C(207) = 188.59e^{0.024*207}\\\Rightarrow C(207) = 188.59e^{4.968}\\\Rightarrow C(207) = 188.59*143.739121458\\\Rightarrow C(207) = 27107.76[/tex]
Thus, the number of cases on November 24, 2014, was approximately 27107.76.
(c) We are asked to find C(92).
This can be found by putting t = 92, in the exponential equation, [tex]C(t) = 188.59e^{0.024t}[/tex].
[tex]C(92) = 188.59e^{0.024*92}\\\Rightarrow C(92) = 188.59e^{2.208}\\\Rightarrow C(92) = 188.59*9.09750317953\\\Rightarrow C(92) = 1715.70[/tex]
Thus, C(92) = 1715.70.
This means that on the 92nd day from May 1, 2014, the number of Ebola cases in Africa was approximately 1715.70.
The complete question is:
"The spread of the Ebola virus in Africa in 2014 could be modeled by [tex]C(t) = 188.59e^{0.024t}[/tex] where C represents the number of cases and t represents the number of days since May 1, 2014. (source: http://www.geert.io/exponential-growth-of-ebola.html)
a. [3 pts] Approximately how many cases were there on May 1, 2014?
b. [3 pts] How many cases were projected by November 24, 2014?
c. [4 pts] Find C(92) and explain what it means in the context of the problem.
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