Теория систем и системный анализ (1088583), страница 8
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Построим график
2.4.6. Логарифмическая модель.
По значениям в таблице ищем A1 и A2:
| Логарифмическая |
| ||
|
| a1 = | 71,89550652 | |
|
| a2 = | -1,234852789 | |
|
| 1355 | 1355 | |
|
| 4661,367137 | 4661,367138 | |
| x | y=a1+a2*ln(x) |
| 20 | 68,19621817 |
| 21 | 68,1359695 |
| 22 | 68,07852413 |
| 23 | 68,02363274 |
| 24 | 67,97107788 |
| 25 | 67,92066873 |
| 26 | 67,87223692 |
| 27 | 67,82563317 |
| 28 | 67,78072449 |
| 29 | 67,73739187 |
| 30 | 67,69552845 |
| 31 | 67,65503784 |
| 32 | 67,61583288 |
| 33 | 67,57783441 |
| 34 | 67,54097039 |
| 35 | 67,50517505 |
| 36 | 67,47038817 |
| 37 | 67,43655447 |
| 38 | 67,40362311 |
| 39 | 67,3715472 |
| A | B | C | |
| 26 | Логарифмическая |
| |
| 27 |
| a1 = | 71,89550652 |
| 28 |
| a2 = | -1,234852789 |
| 29 |
| =20*C27+C28*L22 | =B22 |
| 30 |
| =C27*L22+C28*M22 | =P22 |
| F | G | |
| 26 | x | y=a1*x^a2 |
| 27 | 20 | =$C$27+$C$28*LN(E27) |
| 28 | 21 | =$C$27+$C$28*LN(E28) |
| 29 | 22 | |
| 30 | 23 | |
| 31 | 24 | |
| 32 | 25 | |
| 33 | 26 | |
| 34 | 27 | |
| 35 | 28 | |
| 36 | 29 | |
| 37 | 30 | |
| 38 | 31 | |
| 39 | 32 | |
| 40 | 33 | |
| 41 | 34 | |
| 42 | 35 | |
| 43 | 36 | |
| 44 | 37 | |
| 45 | 38 | |
| 46 | 39 |
Построим график
2.4.7. Показательная модель.
По значения в таблице ищем A1 и A2:
| Показательная |
| |
|
| a1 = | 6,007331346 |
|
| a2 = | 1,082210138 |
|
| 82,15676178 | 82,15676178 |
|
| 2461,248597 | 2461,248597 |
| x | y=a1*a2^x |
| 20 | 29,16846341 |
| 21 | 31,56640683 |
| 22 | 34,16148551 |
| 23 | 36,96990596 |
| 24 | 40,00920705 |
| 25 | 43,2983695 |
| 26 | 46,85793445 |
| 27 | 50,71013173 |
| 28 | 54,87901868 |
| 29 | 59,3906304 |
| 30 | 64,27314235 |
| 31 | 69,55704629 |
| 32 | 75,27534069 |
| 33 | 81,46373687 |
| 34 | 88,16088196 |
| 35 | 95,40860027 |
| 36 | 103,2521545 |
| 37 | 111,7405284 |
| 38 | 120,9267327 |
| 39 | 130,8681362 |
| A | B | C | ||
| Показательная |
| |||
| 28 |
| a1 = | 6,007331346 | |
| 29 |
| a2 = | 1,082210138 | |
| 30 |
| =LN(C27)*20+LN(C28)*A22 | =K22 | |
| 31 |
| =LN(C27)*A22+LN(C28)*C22 | =L22 | |
| F | G | |
| 26 | x | y=a1*a2^x |
| 27 | 20 | =$C$27*$C$28^F27 |
| 28 | 21 | =$C$27*$C$28^F28 |
| 29 | 22 | |
| 30 | 23 | |
| 31 | 24 | |
| 32 | 25 | |
| 33 | 26 | |
| 34 | 27 | |
| 35 | 28 | |
| 36 | 29 | |
| 37 | 30 | |
| 38 | 31 | |
| 39 | 32 | |
| 40 | 33 | |
| 41 | 34 | |
| 42 | 35 | |
| 43 | 36 | |
| 44 | 37 | |
| 45 | 38 | |
| 46 | 39 |
Построим график
2.4.8. Экспоненциальная модель.
По значения в таблице ищем A1 и A2:
| Экспоненциальная |
| |
|
| a1 = | 6,007331346 |
|
| a2 = | 0,079005375 |
|
| 82,15676178 | 82,15676178 |
|
| 2461,248597 | 2461,248597 |
| x | y=a1*e^(a2*x) |
| 20 | 29,16846341 |
| 21 | 31,56640683 |
| 22 | 34,16148551 |
| 23 | 36,96990596 |
| 24 | 40,00920705 |
| 25 | 43,2983695 |
| 26 | 46,85793445 |
| 27 | 50,71013173 |
| 28 | 54,87901868 |
| 29 | 59,3906304 |
| 30 | 64,27314235 |
| 31 | 69,55704629 |
| 32 | 75,27534069 |
| 33 | 81,46373687 |
| 34 | 88,16088196 |
| 35 | 95,40860027 |
| 36 | 103,2521545 |
| 37 | 111,7405284 |
| 38 | 120,9267327 |
| 39 | 130,8681362 |
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