ACTIVITY 1.1 Solve the following problems. Show your complete solutions. For numbers 1 and 2. The population of a certain animal in an area is represented by the equation y =750(0.95) where t is the number of years since year 2000. 1. In the given equation, a. What does 750 represent? b. What does 0.95 represent? 2. Compute the predicted population of a certain animal in the year 2010. Round your answer to nearest whole number. For numbers 3 and 4. A computer valued P150,000 depreciates at the rate of 12.3% per year. 3. Write a function that models the value of the computer. 4. Find the value of the computer after four years. RO_ GeneralMathematics_Grade11_Q1_LP 7 ACTIVITY 1.2 Solve the following problems. Show your complete solutions. 1. The first year of a charity walk event in a certain city had an attendance of 200 people. The attendance y increases by 5% each year. a. Write an exponential growth function to represent this situation. b. How many people will attend in the sixth year? Round your answer to the nearest person. 2. The yearly profits of a certain small company is 500,000. The profits have been decreasing by 4% per year. a. Write an exponential decay function to represent this situation. b. What will be the profits in 5 years? Round your answer to the nearest pesos. 3. You deposit P10,000 in a savings account that earns 3% annual interest compounded once a year. a. Write a function that represents the balance after t years. b. How much money do you have at the end of 6 years? Round your answer to the nearest pesos.A. Exponential Growth Functions A function of the form y = a(1+r)', where a > 0 and r > 0, is an exponential growth function. Exponential growth occurs when a quantity increases by the same rate rin each period t When this happens, the value of the quantity at any given time can be calculated as a function of the rate and the original amount. initial amount rate of growth (in decimal form) final amount ry' time growth factor Example 1. The inaugural attendance of an annual music festival in a certain country is 120,000. The attendance y increases by 6% each year. a. Write an exponential growth function that represents the attendance after t years. b. How many people will attend the festival in the fourth year? Round your answer to the nearest thousand. Solution: a. The initial amount is 120,000 and the rate of growth is 6% or 0.06 y = a(1 + n) Write the exponential growth function. = 120,000(1 + 0.06)' Substitute 120,000 for a and 0.06 for r. = 120,000(1.06)' Add. The festival attendance can be represented by y = 120,000(1.06)'. b. The value t = 3 represents the fourth year because = 0 represents the first year. y = 120,000(1.06)' Write the exponential growth function. = 120,000(1.06)3 Substitute 3 for t. = 142,922 Use a calculator. About 143,000 people will attend the music festival in the fourth year. B. Exponential Decay Functions A function of the form y = a(1 - r) , where a > 0 and 0