Asked by Tesla
Which is the graph of the sequence defined by the function f(x) = 100(0.5)x - 1?
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Answered by
GPT-5 mini
AI
I need to check the intended meaning of the notation. There are two common interpretations:
1) If you mean f(x) = 100·(0.5)^x − 1 (a geometric/exponential sequence):
- The graph is a set of discrete points at integer x (x = 0,1,2,...) with values
f(0)=99, f(1)=49, f(2)=24, f(3)=11.5, ...
- The points decrease rapidly (each step roughly halves the previous value minus 1) and approach the horizontal asymptote y = −1 from above. So you get a decreasing exponential-looking cloud of points that levels off at y = −1.
2) If you mean f(x) = 100·(0.5)x − 1 = 50x − 1 (i.e., 0.5 multiplied by x, a linear function):
- The graph is a straight line with slope 50 and y-intercept −1 (discrete points if this is a sequence, otherwise a continuous line).
If you tell me which interpretation your problem uses (exponent or multiplication by x), I can give or draw the precise graph.
1) If you mean f(x) = 100·(0.5)^x − 1 (a geometric/exponential sequence):
- The graph is a set of discrete points at integer x (x = 0,1,2,...) with values
f(0)=99, f(1)=49, f(2)=24, f(3)=11.5, ...
- The points decrease rapidly (each step roughly halves the previous value minus 1) and approach the horizontal asymptote y = −1 from above. So you get a decreasing exponential-looking cloud of points that levels off at y = −1.
2) If you mean f(x) = 100·(0.5)x − 1 = 50x − 1 (i.e., 0.5 multiplied by x, a linear function):
- The graph is a straight line with slope 50 and y-intercept −1 (discrete points if this is a sequence, otherwise a continuous line).
If you tell me which interpretation your problem uses (exponent or multiplication by x), I can give or draw the precise graph.
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