What is the value of k for the decreasing volume of chlorine in a swimming pool?

[rachael]

13 The volume of chlorine, C litres, in a swimming pool at time t hours after it was placed in
the pool can be modeled by C(t) = C0e^kt, t ≥ 0. The volume of chlorine in the pool is
decreasing. Initially the volume of chlorine in the pool was 3 litres, 8 hours later the
volume was 2.5 litres.

b Find the exact value of k.
i tried to work this question out but it do not turned out to be right.
i used C(t)=3e^kt
where c(t)=3
then there is another equation C(t)=2.5e^8t
then i used simultanoeus equation
is this method correct?



thank you

 

[VietDao29]

13 The volume of chlorine, C litres, in a swimming pool at time t hours after it was placed in
the pool can be modeled by C(t) = C0e^kt, t ≥ 0. The volume of chlorine in the pool is
decreasing. Initially the volume of chlorine in the pool was 3 litres,

This means C(0) = 3. Plug it in the expression for C(t), we have:
C(t) = C(0)e^kt = 3e^kt, right?

8 hours later the
volume was 2.5 litres.

This means that C(8) = 3e^k8 = 2.5
From here, can you solve for k?
By the way, this can be done exactly in the same way as this problem.
Can you go from here? :)

 

[rachael]

thank you
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