Answer each of the problems. Make sure to show all your work. The number of students at a school increases at a rate proportional to its current size. In 2005, the school had 1700 students. In 2009, the school had 1850 students. Answer the following. 1) Write a differential equation that models this situation. Let P represent the student population and let t represent the number of years since 2005. 2) Solve for the general solution. 3) Solve for the particular solution in terms of P and t (find the values of all constants). 4) Determine what year the school's population will reach 2100. 5) Determine the rate at which the population is increasing in 2010. Include units in your answer.The median value of a home in a particular market is decreasing exponentially. If the value of a home was initially $240,000, then its value two years later is $235,000. Answer the following. 6) Write a differential equation that models this situation. Let V represent the value of the home (in thousands of dollars) and t represent the number of years since its value was $240,000. 7) Solve for the particular solution in terms of V and t (find the values of all constants). 8) Determine when the value of the home will be 90% of its original value. 9) Determine the rate at which the value of the home is decreasing one year after it is valued at $235,000. Include units in your answer, and round the final value to the nearest dollar. 10) The relative rate of change in a quantity is defined as the rate of change for that quantity divided by the quantity present. Find the relative rate of change in the home's value at any time t