The yearly cost in dollars, y, at a video game arcade based on total game tokens purchased, x, is y = y equals StartFraction 1 O
2 answers:
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Option C: –10, –7.5, –5, –2.5, … is the sequence that could be partially defined by the recursive formula
Explanation:
The given recursive formula is for
and
We need to determine the sequence.
The sequence can be determined by substituting n = 1, 2, 3, 4,....
<u>2nd term of the sequence:</u>
Substituting n = 1 in the formula , we get,
Simplifying, we have,
Thus, the 2nd term of the sequence is -7.5
<u>3rd term of the sequence:</u>
Substituting n = 2 in the formula , we get,
Simplifying, we have,
Thus, the 3rd term of the sequence is -5
<u>4th term of the sequence:</u>
Substituting n = 3 in the formula , we get,
Simplifying, we have,
Thus, the 4th term of the sequence is -2.5
Therefore, the sequence is –10, –7.5, –5, –2.5, …
Hence, Option C is the correct answer.
We will use u-substitute:
Then for substitution:dx=u du. and integral becomes:
=u-ln(u+1)=
. Now we will change the values of limits: 
=4-ln(5)-2+ln(3)=2+ln(0,6)=2-0.51=1.49