SOLUTION: Find the associated exponential decay or growth model. Q = 1,800 when t = 0; half-life = 5

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Question 843241: Find the associated exponential decay or growth model.
Q = 1,800 when t = 0; half-life = 5
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
Solve this generally for k: A=Qe%5E%28-kt%29;
Let t=5, A=(1/2)Q, , and find the formula this way for k.
Rewrite A=1800e%5E%28-k%2At%29 using the value you found for k.


Best if you follow that and do it.
I did not show you the specific steps. Do you need them?


SOLUTION WITH NEARLY ALL STEPS SHOWN--------------------------------
highlight_green%28A=Qe%5E%28-kt%29%29------Basic Model for Decay
ln%28A%29=ln%28Q%29%2Bln%28e%5E%28-kt%29%29
ln%28A%29-ln%28Q%29=-kt%2A1
highlight_green%28k=%28ln%28Q%29-ln%28A%29%29%2Ft%29

The specific example has initial half life of 5 years, t=5 with A=Q%2F2, enough for finding the value of k.
k=ln%28Q%2FA%29%2Ft
k=ln%28Q%2F%28Q%2F2%29%29%2F5
highlight_green%28k=ln%282%29%2F5%29
But as a decimal number, this can be stated highlight%28k=0.1386%29

The specific model equation based on given Q=1800 and the found value for k, becomes highlight%28highlight%28A=1800%2Ae%5E%28-0.1386%2At%29%29%29