SOLUTION: 13. A population of rare birds, P sub t, can be modeled by the equation P sub t, P0e^kt, where Psub0 is the initial population, and t is measured in decades. After one decade, it i

Algebra ->  Functions -> SOLUTION: 13. A population of rare birds, P sub t, can be modeled by the equation P sub t, P0e^kt, where Psub0 is the initial population, and t is measured in decades. After one decade, it i      Log On


   

Question 1104200: 13. A population of rare birds, P sub t, can be modeled by the equation P sub t, P0e^kt, where Psub0 is the initial population, and t is measured in decades. After one decade, it is estimated that Psub1/Psub0 = 0.9.
(i) Find the value of k.
(ii) Interpref the meaning of the value of k.
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
Time t in decades
Only needed is ratio between P and P%5Bo%5D
e, you know

e%5E%28kt%29=P%2FP%5Bo%5D
If t=1;
e%5E%28k%2A1%29=0.9
ln%28e%5Ek%29=ln%280.9%29
k%2A1=-0.10536
highlight%28k=-0.10536%29---------and is negative, for exponential decay

Model equation becomes highlight_green%28P=P%5Bo%5De%5E%28-0.1054%2At%29%29
(Depending on what accuracy you want for k)