ABSTRACT
D 5 (1.28402541 . . . 0.77880078 . . .
1.28402541 . . .C 0.77880078 . . . )
D 5 (0.5052246 . . .
2.0628261 . . .
D 1.2246, correct to 4 decimal places
Problem 4. The instantaneous voltage v in a capacitive circuit is related to time t by the equation v D Vet/CR where V, C and R are constants. Determine v, correct to 4 significant figures, when t D 30 ð 103 seconds, C D 10 ð 106 farads, R D 47 ð 103 ohms and V D 200 volts
Using a calculator, v D 200e0.0638297... D 2000.9381646 . . . D 187.6 volts
Now try the following exercise
Exercise 46 Further problems on evaluating exponential functions
In Problems 1 and 2 use a calculator to evaluate the given functions correct to 4 significant figures:
1. (a) e4.4 (b) e0.25 (c) e0.92 [(a) 81.45 (b) 0.7788 (c) 2.509]
2. (a) e1.8 (b) e0.78 (c) e10 [(a) 0.1653 (b) 0.4584 (c) 22030]
3. Evaluate, correct to 5 significant figures:
(a) 3.5e2.8 (b) 6 5
e1.5 (c) 2.16e5.7
[(a) 57.556 (b) 0.26776 (c) 645.55] 4. Use a calculator to evaluate the following,
correct to 5 significant figures: (a) e1.629 (b) e2.7483 (c) 0.62e4.178 [(a) 5.0988 (b) 0.064037 (c) 40.446]
In Problems 5 and 6, evaluate correct to 5 decimal places:
5. (a) 1 7
e3.4629 (b) 8.52e1.2651 (c) 5e 2.6921
3e1.1171[ (a) 4.55848 (b) 2.40444 (c) 8.05124
6. (a) 5.6823 e2.1347
(b) e 2.1127 e2.1127
(c) 4e 1.7295 1 e3.6817[ (a) 48.04106 (b) 4.07482
(c) 0.08286 ]
7. The length of a bar, l, at a temperature is given by l D l0e˛, where l0 and ˛ are constants. Evaluate l, correct to 4 significant figures, when l0 D 2.587, D 321.7 and ˛ D 1.771 ð 104.
