Idec
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Say my IQ is 100 and it increases by 1% every day. How high will my IQ be in 23000 days?
We can treat this as compound growth:
IQ(t)=100×(1.01)23000\text{IQ}(t) = 100 \times (1.01)^{23000}IQ(t)=100×(1.01)23000
Compute the exponent in logarithmic form to avoid gigantic numbers:
ln(1.01)≈0.00995033\ln (1.01) \approx 0.00995033ln(1.01)≈0.00995033
23000×0.00995033≈228.857623000 \times 0.00995033 \approx 228.857623000×0.00995033≈228.8576
Add ln(100)=4.60517\ln(100) = 4.60517ln(100)=4.60517:
ln(IQ)≈233.4628\ln(\text{IQ}) \approx 233.4628ln(IQ)≈233.4628
Convert back from natural log:
IQ=e233.4628\text{IQ} = e^{233.4628}IQ=e233.4628
Convert to base 10 scale:
log10(IQ)=233.46282.302585≈101.41\log_{10}(\text{IQ}) = \frac{233.4628}{2.302585} \approx 101.41log10(IQ)=2.302585233.4628≈101.41
So:
IQ≈10101.41≈2.6×10101\text{IQ} \approx 10^{101.41} \approx 2.6 \times 10^{101}IQ≈10101.41≈2.6×10101
Final Answer
Your IQ after 23,000 days at 1% growth per day would be roughly
2.6×10101\boxed{2.6 \times 10^{101}}2.6×10101.
That is an unimaginably large number—far beyond anything physically meaningful for IQ, but mathematically that’s the result.
We can treat this as compound growth:
IQ(t)=100×(1.01)23000\text{IQ}(t) = 100 \times (1.01)^{23000}IQ(t)=100×(1.01)23000
Compute the exponent in logarithmic form to avoid gigantic numbers:
ln(1.01)≈0.00995033\ln (1.01) \approx 0.00995033ln(1.01)≈0.00995033
23000×0.00995033≈228.857623000 \times 0.00995033 \approx 228.857623000×0.00995033≈228.8576
Add ln(100)=4.60517\ln(100) = 4.60517ln(100)=4.60517:
ln(IQ)≈233.4628\ln(\text{IQ}) \approx 233.4628ln(IQ)≈233.4628
Convert back from natural log:
IQ=e233.4628\text{IQ} = e^{233.4628}IQ=e233.4628
Convert to base 10 scale:
log10(IQ)=233.46282.302585≈101.41\log_{10}(\text{IQ}) = \frac{233.4628}{2.302585} \approx 101.41log10(IQ)=2.302585233.4628≈101.41
So:
IQ≈10101.41≈2.6×10101\text{IQ} \approx 10^{101.41} \approx 2.6 \times 10^{101}IQ≈10101.41≈2.6×10101
Final Answer
Your IQ after 23,000 days at 1% growth per day would be roughly
2.6×10101\boxed{2.6 \times 10^{101}}2.6×10101.
That is an unimaginably large number—far beyond anything physically meaningful for IQ, but mathematically that’s the result.
Final Answer
