Page 210 - Start Up Mathematics_8 (Non CCE)

EXERCISE 13.4

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
14
the 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.

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 what it is when it is new. 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 the
1
2
n
Ê R ˆ Ê R ˆ Ê R n ˆ
2
1
depreciated asset value after n years = P 1- 100¯ Ë 1- 100¯ ˜ ...... 1- 100¯ .
˜
˜ Á
Á
Á
Ë
Ë
Example 22: 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
Let the value of the house after 2 years be A.
R
Ê
Ê
20 ˆ
ˆ
A = P 1- 100¯ n = 50,00,000 1- 100¯ 2
Á
˜
Á
˜
Ë
Ë
Ê
= 50,00,000 1- 1ˆ ˜ 2 = 50,00,000 Ê 4ˆ 2
Á ˜
Á
5¯
Ë
Ë
5¯
4 4
= 50,00,000 × × = ` 32,00,000
5 5
The builder gets ` 32,00,000 for the house after 2 years.
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