In the first 6 months of an outbreak, the total number of reported cases could be approximated by C(t) = 95.9e0.71t (0 sts 6), where t is time in months since April 1, 2014. (a) Calculate the average rates of change of C(t) over the successive 2-month periods [0, 2], [1, 3], [2, 4], [3, 5], and [4, 6]. (Round answers to two decimal places.) rate of change over [0, 2] = rate of change over [1, 3] = rate of change over [2, 4] = rate of change over [3, 5] = rate of change over [4, 6] = (b) What kind of model would best describe the successive rates of change obtained in part (a): linear, quadratic, or exponential? O linear O quadratic O exponential What does your answer you about the outbreak? (Round your answer to two decimal places.) The 2-month average rate of increase in the number of the outbreak cases increased by a factor of about each month. Enter a number.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.