\fQuestion 14 (3 points) 4X What is the average value of f(x), between x = 0 and x = 3 for (x) = ( 2x 2+1 ) ?\fSuppose the rate at which the volume in a tank decreases is proportional to the square root of the volume 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 V represent the volume (in gallons) in the tank and t represent the time (in minutes). 2) Solve for the general solution (do not solve for V). 3) Use the initial condition to find the constant of integration, then write the particular solution (do not solve for V). 4) Use the second condition to find the constant of proportion.5) Find the volume at t = 5 minutes. Round your answer to two decimal places.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 the time (in years). 7) Solve for the general solution (do not solve for c). 8) Use the initial condition to find the constant of integration, then write the particular solution (do not solve for c). 9) Use the second condition to find the constant of proportion.The velocity of a particle varies directly as the product of its position and time squared. The particle has known positions s(0) = 3 and s(2) = 5. Answer the following. 11) Write a differential equation that models this situation. Let s represent the position of the particle and t represent the time. 12) Solve for the general solution. Write your answer as a function s(t). 13) Use the initial condition to find the constant of integration, then write the particular solution as a function s(t). 14) Use the second condition to find the constant of proportion. Round your answer to five decimal