How do you answer this question? Can you use log?

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1 Answer
Feb 25, 2018

Read below.

Explanation:

Here is what the question is telling you:

At the beginning, the tank is full of water with #V_0=2000#

There is #2000# units of water to start with.

Every hour, there is #2%# less water than at the start of hour.

Whatever you have at the beginning of the hour, you are subtracting the #2%# of it at the end of the hour.

For example, if I were to start with #x# units of water, then at the end of the hour there is #1x-0.02x# of water, which is #0.98x#

This tells us that at the end of hour, we are left with #98%# of what we had at the beginning of hour.

Therefore, we can say that:

#V_(t+1)=0.98V_t#

#k=0.98#

Using this, let's figure out the first five hours.

#V_0=2000#

#V_1=1960#

#V_2=1920.8#

#V_3=1882.384#

#V_4=1844.73632#

#V_5=1807.8415936#

Hmm... This doesn't help much...

However, we notice that we have to multiply #0.98# once to #2000# to get #V_1#, twice to get #V_2#, and so on.

This can be written as:

#V=2000*0.98^t#

Whatever #t# is, we are multiplying 0.98 that many times to 2000.