A couple seeking to buy a home decides that a monthly payment of $1600 fits their budget. The amount they can borrow, A, is a function of the time t, in years, it will take to repay the debt. If we denote this function by  A = f(t),  then the following table defines the function. t A t A 5 80,000 20 199,000 10 135,000 25 217,000 15 173,000 30 229,000 (a) Find f(20). f(20) = Write a sentence that explains its meaning. It will take this number of years to pay off a debt of 20 thousand dollars.The couple must repay this much per year for every $20 borrowed.     The couple can reduce their payments by $20 if they reduce the amount they borrow by this much.It will take 20 years to pay off a debt of this amount. (b) Does f(5 + 5) = f(5) + f(5)? Explain. Yes, because f(5 + 5) = f(10) and f(5) + f(5) = f(10).Yes, because f(5 + 5) = f(25) and f(5) + f(5) = f(25).     No, because f(5 + 5) = f(10) which is not equal to f(5) + f(5).No, because f(5) + f(5) = f(25) which is not equal to f(5 + 5). (c) If the couple is looking at a house that requires them to finance $173,000, how long must they make payments? Write this correspondence in the form A = f(t), where t is measured in years. $173,000 = f

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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.