Solve the solution.

Question

Solve the solution.

                                                                                                                      x-1992

A city's population P in thousands during year X is modeled by P(x) = 129(1.017)           .  Estimate the year

 

when the city's population reached 139 thousand.

 

In what year did the population reach 139 thousand?

 

(round down to the nearest year as needed.)

Answer 1

P(x) = 129(1.017)^(x-1992)

 

139 = 129(1.017)^(x-1992)

 

(1.017)^(x-1992) = 139/129

 

(x-1992) log(1.017) = log(139/129)

 

x-1992 = (log(139/129))/(log(1.017))

 

x = 1992 + (log(139/129))/(log(1.017))

 

x ≈ 1996.42908051684203 ≈ 1996

Answer 2

P(x ) = 129( 1.017)^( X - 1992)

 

139 = 129 ( 1.017) ^( X - 1992)

 

139/ 129 = ( 1.017) ^ ( X - 1992)

 

 ( X -1992) log 1.017 = log ( 139/ 129)

 

  X - 1992 = Log ( 139/ 129)/ log 1.017 =

 

  X - 1992 = 4. 43

 

  X = 1992 + 4.43 = 1996. 43

 

    Test:

 

     129 * ( 1.017) ^ 4.43 = 139.002

Answer 3

Keith you need to "clean" up the model equation it's not clear what it is.

Jim