In 2000 the population of a country reached 1 billion, and in 2025 it is projected to be 1.5 billion.

Question

In 2000 the population of a country reached 1 billion, and in 2025 it is projected to be 1.5 billion.

 

 

                                                               x- 2000

(a) find values for C and a so that P(x) =Ca            models the population of a country in year x. 

(b) Estimate the country's population in 2010.

(c) Use P to determine the year when the country's population might reach 1.7 billion.

 

(a) C = ? (type an integer or decimal rounded to five decimal places as needed)

(b) Country's population in 2010 is  ?

(c) year country's population might reach 1.7 billion is ?

Answer 1

P(x)  = C a ^ ( X - 2000)

 

C = 1b = 10^9

 

a)  p( X ) = 10 ^9 a ^ ( X - 2000)

 

  1. 5 * 10^6 = 10 ^6 a^ 25

 

     1. 5 = a ^ 25

 

       log 1.5 = 25 log a

 

          a =10 ^( log 1.5 / 25 )= 1.0164

 

        P ( x ) =  ( 1.0164b ) ^  ( X- 2000)

 

   b)      P ( 10 ) = ( 1. 0164 ) ^10  = 1. 1766 billion

 

       c)    1.7 b = 1.0164^ n

           

            n log ( 1.0164)= log1.7

 

           n = log 1.7 / log (1. 0164) = 32.6

 

        approximately @ year 2033