Social Security Monthly social security benefits differ with the age a recipient decides to start receiving benefits. Recipients whose monthly benefits are$2000, if benefits start being paid at a full retirementage of 66, can have their benefits increase by $160per month for each year after 66 they delay startingtheir benefits. Note that the monthly benefit does notincrease if the starting age is after 70. a. Write the linear function that models the monthlybenefit y as a function of age x at which benefitsare started, for the starting ages from 66 to 70.b. What monthly benefit would these recipientsreceive if they started receiving benefits at age 70?(Source: Social Security Administration)

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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.