The population P (in thousands) of a certain city from 2000 through 2014 can be modeled by P = 140.5ekt, where t represents the year, with t = 0 corresponding to 2000. In 2008, the population of the city was about 169,025. (a) Find the value of k. (Round your answer to four decimal places.) k = Is the population increasing or decreasing? Explain. O Because k is negative, the population is increasing. O Because k is negative, the population is decreasing. O Because k is positive, the population is increasing. O Because k is positive, the population is decreasing. (b) Use the model to predict the populations of the city (in thousands) in 2020 and 2025. (Round your answers to three decimal places.) 2020 P = thousand people 2025 P = thousand people Are the results reasonable? Explain. O The populations are reasonable if it continues to increase at the same rate from the year 2020 to 2025. O The populations are not reasonable. The population cannot continue to increase at the same rate it did from the year 2020 to 2025. (c) According to the model, during what year will the population reach 260,000? Read I

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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.