Out-of-pocket spending in a country for health care increased between 2002 and 2006. The function f(x)= 2576 e 0.0359x models average annual expenditures per​ household, in dollars. In this​ model, x represents the​ year, where x=0 corresponds to 2002. (a) Estimate​ out-of-pocket household spending on health care in 2006. ​(b) Determine the year when spending reached ​$2851 per household.

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A: Topic:- derivatives

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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.