Chapter 1.05

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#3
#4
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#33 MTH/MTHT
#34

QA: Can you recite powers of 2 up to 2^16: 1, 2, 4, 8, 16, 32, . . . ? Practice!

QB: with an x window of [0,10] 
i)   graph x   * exp(-x) ; 
ii)  graph x^2 * exp(-x) ; 
iii) graph x^3 * exp(-x) ; 
iv)  graph x^4 * exp(-x) ; 
v) now, what is an appropriate x window for x^20 * exp(-x) ? 
vi) Describe how the shape changes as the power grows.

QC: 
i) Repeat problem 34 using 1/(1+exp(b*x+d)) ; 
ii) if d=3, what must "a" equal to get the same curve? 
iii) if a=4, what must d equal to get the same curve? 
BTW, these types of functions are called "logistic" functions, not to be confused with "log"=logarithm functions.

QD: 
i) repeat problem 34 using 1/(1+exp(b*(x-c))); 
ii) if d=3 and b=2, what must c be to get the same curve? 
iii) if b=2&c=7, what must d be? 
iv) What short phrase describes c? b?