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6 days ago

Wanahton purified a portion of water with 900 grams of contaminants. Each hour, a third of the contaminants was filtered out.

Mathematics

1 answer:

Inessa [9K]6 days ago

8 0

Answer:

B. This is a geometric sequence.

$g(n)=900\cdot (\frac{2}{3})^{n-1}$

Step-by-step explanation:

The problem states that Wanahton treated water containing 900 grams of impurities. Every hour, one-third of these impurities is removed.

After each hour, the remaining impurities reduce to two-thirds of what was present the previous hour since one-third has been eliminated.

As the total is not constant, it thus forms a geometric sequence.

The explicit formula for a geometric sequence can be expressed in the format $a(n)=a\cdot r^{n-1}$ , where

a = First term,

r = Common ratio.

In our particular case, $a=900$ and $r=\frac{2}{3}$ , leading us to the required formula:

$g(n)=900\cdot (\frac{2}{3})^{n-1}$

Consequently, the explicit formula for this geometric sequence is $g(n)=900\cdot (\frac{2}{3})^{n-1}$ .

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