Use the data in Tables 3.4 and 3.5 of Example 4 to estimate the rate of change in pressure with respect to time experienced by the runner when she is at an altitude of 13,330 ft. Make use of a forward difference quotient when estimating the required derivatives.

Table 3.4 and 3.5

Table 3.4 t (minutes) 10 20 30 40 60 70 80 11,660 a(t) (altitude) 13,440 12,710 10,000 10,220 10,510 10,980 12,330 13,330 Table 3.5 a (altitude) 11,330 13,330 10,260 15,830 16,230 14,330 738 700 5485 7795 12,330 840 p(a) (pressure) 690 925 1000 821 793 765