@@ -77,7 +77,7 @@ You'll use these NumPy and Matplotlib functions:
7777Your empirical model assumes that the number of transistors per
7878semiconductor follows an exponential growth,
7979
80- $\log(\text{transistor_count })= f(\text{year}) = A\cdot \text{year}+B,$
80+ $\log(\text{transistor \_ count })= f(\text{year}) = A\cdot \text{year}+B,$
8181
8282where $A$ and $B$ are fitting constants. You use semiconductor
8383manufacturers' data to find the fitting constants.
@@ -87,17 +87,17 @@ rate for added transistors, 2, and giving an initial number of transistors for a
8787
8888You state Moore's law in an exponential form as follows,
8989
90- $\text{transistor_count }= e^{A_M\cdot \text{year} +B_M}.$
90+ $\text{transistor \_ count }= e^{A_M\cdot \text{year} +B_M}.$
9191
9292Where $A_M$ and $B_M$ are constants that double the number of transistors every two years and start at 2250 transistors in 1971,
9393
94- 1 . $\dfrac{\text{transistor_count }(\text{year} +2)}{\text{transistor_count }(\text{year})} = 2 = \dfrac{e^{B_M}e^{A_M \text{year} + 2A_M}}{e^{B_M}e^{A_M \text{year}}} = e^{2A_M} \rightarrow A_M = \frac{\log(2)}{2}$
94+ 1 . $\dfrac{\text{transistor \_ count }(\text{year} +2)}{\text{transistor \_ count }(\text{year})} = 2 = \dfrac{e^{B_M}e^{A_M \text{year} + 2A_M}}{e^{B_M}e^{A_M \text{year}}} = e^{2A_M} \rightarrow A_M = \frac{\log(2)}{2}$
9595
96962 . $\log(2250) = \frac{\log(2)}{2}\cdot 1971 + B_M \rightarrow B_M = \log(2250)-\frac{\log(2)}{2}\cdot 1971$
9797
9898so Moore's law stated as an exponential function is
9999
100- $\log(\text{transistor_count })= A_M\cdot \text{year}+B_M,$
100+ $\log(\text{transistor \_ count })= A_M\cdot \text{year}+B_M,$
101101
102102where
103103
@@ -242,7 +242,7 @@ B, A = model
242242Did manufacturers double the transistor count every two years? You have
243243the final formula,
244244
245- $\dfrac{\text{transistor_count }(\text{year} +2)}{\text{transistor_count }(\text{year})} = xFactor =
245+ $\dfrac{\text{transistor \_ count }(\text{year} +2)}{\text{transistor \_ count }(\text{year})} = xFactor =
246246\dfrac{e^{B}e^{A( \text{year} + 2)}}{e^{B}e^{A \text{year}}} = e^{2A}$
247247
248248where increase in number of transistors is $xFactor,$ number of years is
@@ -263,19 +263,19 @@ Here, use
263263to plot the number of transistors on a log-scale and the year on a
264264linear scale. You have defined a three arrays to get to a final model
265265
266- $y_i = \log(\text{transistor_count }),$
266+ $y_i = \log(\text{transistor \_ count }),$
267267
268268$y_i = A \cdot \text{year} + B,$
269269
270270and
271271
272- $\log(\text{transistor_count }) = A\cdot \text{year} + B,$
272+ $\log(\text{transistor \_ count }) = A\cdot \text{year} + B,$
273273
274274your variables, ` transistor_count ` , ` year ` , and ` yi ` all have the same
275275dimensions, ` (179,) ` . NumPy arrays need the same dimensions to make a
276276plot. The predicted number of transistors is now
277277
278- $\text{transistor_count }_ {\text{predicted}} = e^Be^{A\cdot \text{year}}$.
278+ $\text{transistor \_ count }_ {\text{predicted}} = e^Be^{A\cdot \text{year}}$.
279279
280280+++
281281
@@ -324,7 +324,7 @@ comparator,
324324Then, make a prediction for 2017 with ` Moores_law ` defined above
325325and plugging in your best fit constants into your function
326326
327- $\text{transistor_count } = e^{B}e^{A\cdot \text{year}}$.
327+ $\text{transistor \_ count } = e^{B}e^{A\cdot \text{year}}$.
328328
329329A great way to compare these measurements is to compare your prediction
330330and Moore's prediction to the average transistor count and look at the
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