General Direction: Show detailed solution in Part II only. Ensure that the computer graphing software is accessible to everyone. (IN TYPEWRITTEN)

• Mathematical Model for Population Growth (Using Exponential Model):
• Graph from the Software:

Part I. Using the given data, follow the algorithm below to create a mathematical model which describes the population growth of the region. POPULATION REGION 1990 2000 2010 2020 Central Visayas 4,740,318 5,706,953 6,800, 180 8,081,988 1) Compute the difference D in population size during the following year intervals: 1990-2000; 2000-2010: and 2010-2020 2) Use the formula below to get the rate of growth R of each year interval: Let R1990-2000 be the relative growth rate of the 1990-2000-year interval. Its formula is defined as: D1990-2000 R1990-2000 P2000 where D1990-2000 is the difference of the population in 1990 and 2000; and P1990 is the population in 1990. (Express your answers in this part in four decimal places 3) Find the average (arithmetic mean) of the three rates then divide it by 10. The result will serve as the annual relative growth rate r of the region's population. (Express this in four decimal places.) R1990-2000 + R2000-2010 + R2010-2020 r = 3 10 4) Let t = 0 be year 1990, prepare the model for the population growth of your assigned region using the continuous exponential model C(t) = Poert 5) Use answer in #4 to estimate the population size of the region assigned to you in years 2030, 2040, and 2050. (Show only the whole number part of the result.) 6) Using the same model, estimate the year in which the population will reach the 50 and 60 million milestone. (Show only the whole number part of the result.) Part II. Using a computer graphing calculator software (state what software), construct an exponential model that follows the form of either y = A(B)* or y = Aex. Use the two models to estimate the population size of the in years 2030, 2040, and 2050. (Show only the whole number part of the result.)