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1 / 2 100% 1/3 - 100% + H O The number of students at a school increases at a rate proportional to its current size. In 2005, the school Suppose the rate at which the volume in a tank decreases is proportional to the square root of the volume had 1700 students. In 2009, the school had 1850 students. Answer the following. present. The tank initially contains 25 gallons, but has 20.25 gallons after 3 minutes. 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 1) Write a differential equation that models this situation. Let V represent the volume (in gallons) in the ank and t represent the time (in minutes). 2) Solve for the general solution. 2) Solve for the general solution (do not solve for V). for V 3) Use the initial condition to find the constant of integration, then write the particular solution (do not solve 3) Solve for the particular solution in terms of P and t (find the values of all constants). () Use the second condition to find the constant of proportion. 4) Determine what year the school's population will reach 2100. 5) Find the volume at t = 5 minutes. Round your answer to two decimal places. 5) Determine the rate at which the population is increasing in 2010. Include units in your answer. MacBook Air MacBook Air 888 Dll DD 885 FA DD FB F6 DD F7 FO DECXM : C . . M C DE CO . MF|MS M C M c / 1 -4 0 la/1185000_1185500/1185190/b618/29be13edd719209/cf8715d1c52d22eef/1185190.pdf The median value of a home in a particular market is decreasing exponentially. If the value of a home 2 / 3 - 100% + 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. Suppose the cost of an object appreciates at a rate inversely proportional to the sum of its squared cost and 300. The object cost $240 when first purchased, but is worth $45 more after one year. Answer the following. 6) Write a differential equation that models this situation. Let c represent the cost (in dollars) of the object and t represent ")Solve for the particular solution in terms of V and t (find the values of all constants). 7) Solve for the general solution (do not solve for c). 8) Determine when the value of the home will be 90% of its original value. 8) Use the initial condition to find the constant of integration, then write the particular solution (do not solve for c). 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. 9) Use the second condition to find the constant of proportion 10) Find the appreciation rate at f = 1 year. Round your answer to the nearest cent 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. MacBook Air MacBook Air A 00 * 9