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Unformatted text preview: Stewart Calculus ET 5e 0534393217;3. Differentiation Rules; 3.5 The Chain Rule 0.5t 1 ) , it seems that p(t )=0.8 (indicating that 80% of the population
From the graph of p(t )=(1+10e
has heard the rumor) when t 7.4 hours.
t 71. (a) Using a calculator or CAS, we obtain the model Q =ab with a=100.0124369 and
t t ln b b=0.000045145933 . We can change this model to one with base e and exponent ln b [ b =e
t ln b precalculus mathematics or from Section 7.3]: Q =ae
/ =100.012437e from 10.005531t . t x (b) Use Q (t )=ab ln b or the calculator command nDeriv(Y , X , .04) with Y =ab to get
1 1 / Q (0.04) 670.63 A. The result of Example 2 in Section 2.1 was 670 A.
t 20 72. (a) P=ab with a=4.502714 10 and b=1.029953851 ,
where P is measured in thousands of people. The fit appears to be very good. (b) For 1800: m =
1 5308 3929
7240 5308
=137.9 , m =
=193.2 .
2 1810 1800
1800 1790 / So P (1800) (m +m )/2=165.55 thousand people / year.
1 For 1850: m =
1 2 23,192 17,063
31,443 23,192
=612.9 , m =
=825.1 .
2
1850 1840
1860 1850 / So P (1850) (m +m )/2=719 thousand people / year.
1 2 x (c) Use the calculator command nDeriv(Y , X , .04) with Y =ab to get
1 / 1 / P (1800) 156.85 and P (1850) 686.07. These estimates are somewhat less than the ones in part
(b).
(d) P(1870) 41,946.56. The difference of 3.4 million people is most likely due to the Civil War
(1861 1865). 12 ...
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This note was uploaded on 08/02/2011 for the course MATH 1B taught by Professor Reshetiken during the Spring '08 term at University of California, Berkeley.
 Spring '08
 Reshetiken
 Calculus, Chain Rule, The Chain Rule

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