EXPONENTIAL AND LOGARITHMIC FUNCTIONS

PROBLEM 5.

One such study measured the time it took to respond when faced with varying numbers of choices. Experimental results are given in the table below, where N is the number of choices presented and R is the reaction time in seconds. Graph these data on semilogarithmic graph paper with N on the logarithmic scale (or graph R against log(Base 10)N if semilog graph paper is not available) and find an empirical expression for reaction time as a function of the number of choices. Solution: The points are graphed and a "best fit" line drawn (see Fig. 6.3). Since the point (N, R) = (1, 0.17) does lie on this line, we have R = 0.17 + m log(Base 10)N. To find m, we can use the points (1, 0.17) and (9, 0.59), since both are on the "best fit" line:

0.59 = 0.17 + m log 9

so

0.42 = m (0.954),

or
m = (0.42)/(0.954) = 0.44

The requested relation is R = 0.17 + 0.44 log N.

As we have seen in Chapter 4, solar cells, which convert solar energy into electrical energy, can be used to supply power in space vehicles. Nuclear energy derived from radioactive isotopes is also used. Nuclear energy sources gradually lose power in a manner described by the exponential function. The next problem illustrates some computations of the available power and operational life of a satellite using a nuclear power source.

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