The projected number of senior citizens in the U.S. for the years 1995 through 2030 can be modeled by N(X), million senior citizens, where x is the number of years after 2000. N(X) = 0.03x² + 0.315x + 34.23 (a) Find the derivative of N(x) and use it to complete the model statement below. (Refer back to Section 3.2 of your text (or ebook) for simple derivative rules.) N'(x)= 2030. --select units-- gives the projected rate at which the number of senior citizens is changing x years after 2000, for the years 1995 through Use the appropriate function from above to answer questions b through d. (b) What is the projected number of senior citizens in the year 2025? (Round your answers to 3 decimal places.) million senior citizens (c) What is the projected rate of change of the number of senior citizens in 2025? (Round your answers to 3 decimal places.) million senior citizens per year (d) The Census Bureau predicts that in 2030, 20.1% of the U.S. population will be senior citizens. Use this prediction to estimate the total U.S. population in 2030. (Round your answer to 3 decimal places.) million people

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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.