Question

The values of the concentration C of a desired compound in terms of the time t (sec) are given in the
following table

t 3 9 12 18 24 30
C(t) 4.1 4.3 3.9 3.4 3.1 2.7
Assuming that the guess function is C(t) = c + ae−0.47t + be−0.06t

, find the values of a, b and c that

best fit this table.

Answer 1

Answer:

4 ×~°|¶€%{×¢°π^¥^×` kssvsvis182528

Answer 2

given a function C(t)=c+ae-0.47t+be-0.06t and table for values of C(t) and t

Explanation:

1. C(t) is the function that gives concentration of a desired compound in terms of time 't' time in sec and follows the guess function,                              $C(t)=c+ae^{-0.47t}+be^{-0.06t}\ \ \ \ \ \ \ \ \ \ \ \ \ (here,\ e=2.718)$    
2. Table of values for different values of time and corresponding C(t) is:              $t\ \ \ \ \ \-\ 3\ \ \ \ 9\ \ \ 12\ \ 18\ \ 24\ \ 30\\C(t)\ \ 4.1\ 4.3\ 3.9\ 3.4\ 3.1\ 2.7$        
3. putting any three t, C(t) pair of values from the table in the function C(t) we get three equations to solve for three unknowns a, b, and c:  $c+ae^{-1.41}+be^{-0.18}-4.1=0\ \ \ \ \ \ \ \ \ \ \ \ (t=3,\ \ C(t)=4.1)\\c+ae^{-4.23}+be^{-0.54}-4.3=0\ \ \ \ \ \ \ \ \ \ \ \ (t=9,\ \ C(t)=4.3)\\c+ae^{-5.64}+be^{-0.72}-3.9=0\ \ \ \ \ \ \ \ \ \ \ \ (t=12,\ \ C(t)=3.9)$            
4. simplifying we get:                                                                                                                $0.244a+0.83b+c-4.1=0\\0.014a+0.58b+c-4.3=0\\0.003a+0.48b+c-3.9=0$        
5. solving these equations for a, b and c we get,                                                            $a=-5.92\ \ \ \ \ \ \ b=4.65\ \ \ \ \ \ \ c=1.48$