The projected population of a certain ethnic​ group(in millions) can be approximated by ​p(t)=37.79 left parenthesis 1.014 right parenthesis Superscript t37.79(1.014)t where t=0 corresponds to 2000 and 0 less than or equals t less than or equals 500≤t≤50.   a. Estimate the population of this group for the year 2010. b. What is the instantaneous rate of change of the population when t=​10? a. The population in 2010 is nothing million people. ​(Round to three decimal places as​ needed.)

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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.