Page 133 - ICSE Math 8

From (1) and (2), we get

Ï Ê Ô R ˆ 5568 ¸ 3 Ê R ˆ n Ê R ˆ 5568 ¥ 3 Ê R ˆ n
Ô
Ì Á 1- ˜ ˝ = Á 1- ˜ fi 1- ˜ = Á 1- ˜
Á
Ó Ë Ô 100¯ ˛ Ô Ë 100¯ Ë 100¯ Ë 100¯
Ê R ˆ 16704 Ê R ˆ n
fi 1- 100¯ = Á 1- 100¯
˜
Á
˜
Ë
Ë
fi n = 16,704 ( If the bases are the same, we can equate the powers.)
Hence, the age of the wooden piece is 16,704 years.

EXERCISE 11.5

1. The population of a village 2 years ago was 5,000. If the annual growth in population during 2 successive
years was at the rate of 5% and 7% respectively, find the present population of the village.
2. The bacteria in a culture grows by 5% in the first hour, decreases by 5% in the second hour and again
increases by 5% in the third hour. If the original count of bacteria in a sample is 5,000, find the bacteria
count at the end of 3 hours.
3. The population of a village was decreasing every year due to migration, poverty and unemployment. The
present population of the village is 3,15,840. Last year the migration was 4% and the year before last, it
was 6%. What was the population of the village 2 years ago?
4. From a village, people started migrating to nearby cities due to unemployment. The population of the village
2 years ago was 6,000. If its present population is 5,415, find the rate at which the migration is taking place.
5. Carbon-14 (C ) decays at a constant rate in such a way that it reduces to 50% in 5,568 years. Find the
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age of an old wooden piece in which the carbon is only 25% of the original.
6. The population of a town increases at the rate of 50 per thousand. If the estimated population after 2 years
will be 22,050, find the present population of the town.
1
7. The height of a tree increases every year by times. If the present height of the tree is 250 cm, find its
5
height after 3 years.
Depreciation

The value (P) of any asset reduces over a period of time due to usage and wear and tear. For example, the
value of a computer or a machinery reduces with time. The price it fetches after a few years of use will be far
less than its original price. This relative decrease in asset value over a period of time is called depreciation.
The depreciation per unit of time is called the rate of depreciation.
(a) If P is the asset value, R% is the rate of depreciation per annum and n is the number of years, then
Ê R ˆ n
depreciated asset value after n years is P 1- 100¯ .
˜
Á
Ë
(b) If, R %, R %, ......, R % are the rates of depreciation in the 1st, 2nd, ......, nth year respectively, then
1
2
n
Ê R ˆ Ê R ˆ Ê R ˆ
1
n
2
the depreciated asset value after n years = P 1- 100¯ Ë 1- 100¯ ...... 1- 100¯ .
˜
˜ Á
Á
˜
Á
Ë
Ë
Example 20: A builder constructs a house for ` 50,00,000. Due to recession, its value depreciates by 20%
in 2 years. What value does he get, if he sells this house after 2 years?
Solution: Original value of the house (P) = ` 50,00,000, Rate of depreciation (R) = 20%,
Time (n) = 2 years
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