Question 60178
Given  P (t) = 368 * (1.02)^t 


            r = 10^m


           1.02 = 10^m


           Taking log on both sides, we get:


           Log(1.02) = m log(10)


           0.008600 = m (1)


            A = 10^b


            368 = 10^b


           Taking log on both sides, we get:


           Log(368) = b (log 10)


           2.56584   = b


            y = mx +  b


            y = 0.0086 x + 2.56584     --------- EQN(1)               


           Put  x = 60 ( 1950 + 60 = 2010 ) in the above equation, we get


           y = 0.0086 (60) + 2.56584 = 0.516 + 2.56584 = 3.08184

           
           y ≈ 3. 1 million



           b. Use the function to determine the year during which the population of India will reach 2 billion.


           Solution:  Consider   the equation (1), we get:


                             y = 0.0086 x + 2.56584 

       
                             When y =2 billion,


                             2 = 0.0086 x  + 2.56584


                             -0.56584 / 0.0086 = x


                              -65.795 = x


        The year when the population will be 2 million is  

 
        1950  - 65.79 =  1885