[R] How to regress data into coefficients for a gamma function

[Walter Anderson]

  Hello,

I need to regress data like the example below.  The data points 
represent friction factors derived from observed trip length data.  The 
function used to describe this data is a gamma function of the form, 
f(t) = a * t^b * e^(c*t)  and I need to regress the data to obtain the 
a,b, and c coefficients.  The gamma function can also be expressed in 
the log-linear form, ln[f(t)] = ln[a] + b * ln[t] + c*t, which may be 
easier to perform a regression on.  I have performed a search for 
information on the subject, and have found a few possibly related sites, 
I can not figure out how to perform the regression in R.  Any 
help/guidance would be appreciated.

Walter

            t                f      ln(f)
   1      1    952893    13
   2      2    951077    13
   3      3    945991    13
   4      4    942358    13
   5      5    939452    13
   6      6    895494    13
   7      7    891861    13
   8      8    882416    13
   9      9    873697    13
10    10    867885    13
11    11    797771    13
12    12    791595    13
13    13    779243    13
14    14    773068    13
15    15    765802    13
16    16    635383    13
17    17    628481    13
18    18    620488    13
19    19    612859    13
20    20    609590    13
21    21    508597    13
22    22    503511    13
23    23    498425    13
24    24    490069    13
25    25    486073    13
26    26    422862    12
27    27    418866    12
28    28    415233    12
29    29    408331    12
30    30    405424    12
31    31    263380    12
32    32    261201    12
33    33    257204    12
34    34    252845    12
35    35    250665    12
36    36    209978    12
37    37    205981    12
38    38    203438    12
39    39    199079    12
40    40    197263    12
41    41    154758    11
42    42    152942    11
43    43    149309    11
44    44    148583    11
45    45    147493    11
46    46    98086    11
47    47    97723    11
48    48    95906    11
49    49    94090    11
50    50    93363    11
51    51    81738    11
52    52    81012    11
53    53    80649    11
54    54    79559    11
55    55    79195    11
56    56    70477    11
57    57    70477    11
58    58    70477    11
59    59    70477    11
60    60    70477    11
61    61    42867    10
62    62    42140    10
63    63    42140    10
64    64    42140    10
65    65    41777    10
66    66    36691    10
67    67    36328    10
68    68    35965    10
69    69    35965    10
70    70    35965    10
71    71    31968    10
72    72    31968    10
73    73    31968    10
74    74    31968    10
75    75    31605    10
76    76    21070    9
77    77    20707    9
78    78    20707    9
79    79    20343    9
80    80    19980    9
81    81    15984    9
82    82    15984    9
83    83    15984    9
84    84    15984    9
85    85    15984    9
86    86    14168    9
87    87    14168    9
88    88    14168    9
89    89    14168    9
90    90    14168    9