SOLUTION: The population P of a certain town in time t is modulled by the equation p=Ax10^kt,t=greater than or equal to zero where A and K are non zero constants.When t=3,p=1900 and when

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: The population P of a certain town in time t is modulled by the equation p=Ax10^kt,t=greater than or equal to zero where A and K are non zero constants.When t=3,p=1900 and when       Log On


   

Question 1172508: The population P of a certain town in time t is modulled by the equation
p=Ax10^kt,t=greater than or equal to zero where A and K are non zero constants.When t=3,p=1900 and when t=6,p=38000.Find the value of A and K.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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The population P of a certain town in time t is modulled by the equation
p=Ax10^kt, t=greater than or equal to zero where A and K are non zero constants.
When t=3,p=1900 and when t=6,p=38000.
Find the value of A and K.
A%2810%5E%286k%29%29+=+38000
A = 38000%2F10%5E%286k%29
and
A%2810%5E%283k%29%29+=+1900
A = 1900%2F10%5E%283k%29
A=A therefore
38000%2F10%5E%286k%29 = 1900%2F10%5E%283k%29
cross multiply
38000%2810%5E%283k%29%29+=+1900%2810%5E%286k%29%29
%2810%5E%286k%29%29%2F%2810%5E%283k%29%29 = 38000%2F1900
10%5E%286k-3k%29 = 20
10%5E%283k%29 = 20
3k = log(20), (log of 10 is 1)
3k = 1.301
k = 1.301/3
k = .43367
find A
A(10^(1.301)) = 1900
A = 1900%2F10%5E1.301
A = 95
;
A = 95, k = .43367
:
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Check this
95%2810%5E%286%2A.43367%29%29 = 37996.5 ~ 38000