An environmental study has revealed that the water from a factory has polluted the water in a nearby dam. The pollution had an effect on the water lilies growing on the water surface of the dam. At first the polluted water caused the plants to grow profusely and later on it caused the plants to die and the area covered by the plants to decrease. A mathematician established that the surface area, A (in m²), covered by the water lilies can be approximated by the formula A = - 14³ +12t², where t is the time rates classroom in months after the start of the study, with 0≤t≤24. After how many months did the area covered by the water lilies reach a maximum? Calculate the maximum area that was covered by the plants. At what rate was the area increasing one month after the study began? 2.2.1 Use the steps of Polya to solve this problem. You must explain in detail what you are doing in each step.
