The percentage P of light transmitted by n sheets of plastic is given by P = 25 × 22 − n. (a) What percentage is transmitted by 0 sheets? (b) What percentage of light is transmitted by four sheets? (c) How many sheets transmit 0·78125% of light?
Solution P = 25 × 22 − n
(a) n = 0: P = 25 × 22 = 100% (b) n = 4: P = 25 × 2−2 = 6∙25% (c) 0∙78125 = 25 × 22 − n
22 − n = 0·03125 = 1 ___
2 − n = −5 n = 7
Answer: 7 sheets EXERCISE 5
1. Write the following in the form 2k: (a) 4
(b) 16 (c) 128
(d) 84
(e) 8 (f ) 8
__ 3
1
__ 3
4
(g) 1 __
8
__ 3
4 (h) 1
___ 8 − 4
__ 3
(e) 9 − 3 __
2
__ 3
9 (f ) 1 (i) √
___ 32
__ 8
(j) 16 √
__ 3
1
_____ 32
__ 2
(k) 42 × 16 × 2
(l) 2−2 ___
4−1
2. Write the following in the form 3 p: (a) 9 (b) 1
(c) 1 __
(d) 1
___ 9−2
___ 9 − 3
__ 2
(g) (3 √ √
(h) (
__ 3 )4
____ 3
___ 27
) 3 (l)
(i) 3−2 ___
9
(j) 3−2 ___
3−4 (k) 9 (
___ 3−2
___ √
3
__ 3
) 4
_______ 8
__ 2
1
3. Write the following in the form with base 2: (i)
(a) 4 x (b) 1 __ 2 x
(c) ( √ (d) 8x
(e) 16 ___
2x
__ 2 )x
(f ) 2 × 8x (g) 32x
___ 2
(h) (4x )2
(f ) 3x __
__ 9x
9x (
(c) 9−x (d) 1
(g) 9x + 1 ____
3
___ 9−x
(e) 9x + 2
(h) (3x )2 × 3 (i)
( 3x __
9 )
5. Solve the following for x: (a) 4x = 16
(b) 4x = 1 ___
16 2
(c) 4x = 82 (d) 1
___ √
__ 2
2x
(j) 2x ___
24x
(k) 4x + 1 ____
4. Write the following in the form with base 3: (a) 9x (b) 1
