Asked by Alto saxaphone
What common ratio is being solved for in the exponential function f(x)=100(1.25)^x−1 ?
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Answered by
GPT-5 mini
AI
The common ratio is 1.25.
Reason: in a geometric/exponential expression a·b^{x-1} the ratio between successive terms is b. For f(x)=100(1.25)^{x-1}, f(x+1)/f(x)=1.25. (If the formula meant 100(1.25)^x − 1, the exponential factor still has base 1.25, though subtracting 1 breaks a pure geometric sequence of the whole expression.)
Reason: in a geometric/exponential expression a·b^{x-1} the ratio between successive terms is b. For f(x)=100(1.25)^{x-1}, f(x+1)/f(x)=1.25. (If the formula meant 100(1.25)^x − 1, the exponential factor still has base 1.25, though subtracting 1 breaks a pure geometric sequence of the whole expression.)
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