Solve the following problems below. Choose at least 4 problems. 1. Find the equation of the curve that passes through (-4,1) and whose tangent line at any point has slope x + 4. 2. Find the function y = f(t) passing through the point (0,15) with the first derivative = 3. A bacteria culture which started at 2,000 became 6,000 after 4 hours. After how many hours will the bacteria reach 20,000? The number of bacteria increases exponentially. 4. Suppose that a population of a certain type of animals follows the bounded growth model. These animals have a population limit of 10,000. If at time t = 0, there are 4,000 of these animals are after one year, there are 5,000 of these animals. How many are they at t = 4 years? 5. A science teacher is doing an experiment. At the start of the experiment, there were 1,000 bacteria. After an hour, they became 10,000. What is the rate of growth of the bacteria? How many bacteria will there be for the next one hour of experiment? 6. The rate of decay of radium is proportional to the amount present at any time. The half- life of radium is 1690 years and 20 mg of radium are present now. a. If y milligram of radium will be present t years from now, express y as a function of t. b. Estimate how much radium will be present 1000 years from now. 7. A particular office building is said to depreciate 7% each year. If a new office building valued at Php25.000.000. what will it be worth after 6 vears? Note: V = P(1 -r)"