In: Advanced Math
The standard technique for determining cardiac output is the indicator dilution method developed by Hamilton. One end of a small catheter is inserted in the radial artery and the other end is connected to a densitometer which can automatically record the concentration of the dye in the blood. A known amount of dye, 5.6mg is injected rapidly the following data is obtained. Fill in the table using Newton’s interpolation to determine the divided difference coefficients.
t (s) 2 3 8 10 13 14
C (mg/L) 0.89927 0.85987 1.96637 1.54559 0.17987 0.50699
t | C(t) | ∆ f'(x) | ∆ f"(x) | ∆ f"'(x) | ∆ f""(x) | ∆ f""'(x) |
2 | 0.89927 | |||||
3 | 0.85987 | |||||
8 | 1.96637 | |||||
10 | 1.54559 | |||||
13 | 0.17987 | |||||
14 | 0.50699 |