1. ## Algebra Question

A chemical was used to treat the water in a swimming pool.
The concentration of the chemical at 8 am was 200 mg per litre.
The concentration of the chemical in the water reduces by 30 % each hour

It is not safe to swim in the pool which the concentration of the chemical is more than 25 mg per litre.

The concentration "C" mg per litre of the chemical in the water "t" hours after 8 am is given by:

C=200*0.7^t

How many hours after 8 am will it be safe to swim in the pool?

~~~~ FIRST TIME USING MATH TAGS! GOT IT FIRST TIME TRYING!

Is this the right start?:

25=200*0.7^t

If so how do I finishing solving it?

2. $\displaystyle 25 = 200\times 0.7^t$

where $\displaystyle t=0 \implies \text{8 AM}$

$\displaystyle \frac{1}{4} = 0.7^t$

$\displaystyle t = \log_{0.7}\frac{1}{4}$

3. $\displaystyle \frac{1}{4} = 0.7^t$

Can you explain how got to this please? Divide by 200? but's 1/8 not 1/4.

4. correct, was supposed to be 1/8.

5. $\displaystyle t = \log_{0.7}\frac{1}{8}$

stuck on where to go from here.

I tried to solve but got the wrong answer

~~~ SOLVED

I believe last step Pickslides gave me was wrong :$\displaystyle t = \log_{0.7}\frac{1}{4}$

$\displaystyle \log\frac{1}{8} = x\log\ 0.7$