Question

Between April 1st and April 15th, water in a storage tank was being used at a rate of u(x) = 0.014xº - 0.258x? + 1.065x + 3.873 hundred gallons per day, where x is the number of days since the end of March Check: u(3) = 5.124 At the same time, water was being replenished to the tabk at a rate of r(x) = -0.047x + 0.834x² - 4.145x + 7.746 hundred gallons per day, where x is the number of days since the end of March Check: r(3) = 1.548 How did the water level in the tank change between April 1st and April 5th? the eater level increased by 1140.8 gallons the water level decreased by 1140.8 gallons the water level increased by 47.875 gallons the water level decreased by 47.875 gallons

Answer 1

Between April 1st and April 15th, water in a storage tank was being used at a rate of u(x) = 0.014xº - 0.258x? + 1.065x + 3.8

solutions ube) = 0.0148 -0.258x4+1.065x+3.873 Hundred Gallou Perday roo = -0.047x2 +0.8323? 4.145x+7.746 Hundred Gallon per day we have to find the water level in the tank between April 1st to April sth. since the rate of change in water level is given as the difference of water out in water in therefore, dh dx - uc)-rx 0.061863-1.092 x?+5.2 - 217- 3.873 since we have to find the level of water in tank during 1st April to 5th April, integrate this rate of change from SO I to 5 as follows. 5 ha -1,092 2? +5.2 10x - 3.873 1873) dx (0.001 -1.092 +5-210-2.8733) 56.00 -0.061 -1.099, +5.21061 -3-873 * 3x)} 25 625 4 125 +1.092 3 +5.210 3.87345

= 11. 408 since, the amount of water used is greater than amount of water in. Hence, the required level of water is decreased 1140.8 gallous. by 1 - option 2 is Correct