Page 78 - ICSE Math 7

Example 21: A school uses a phone tree to contact each students’ family to inform about an upcoming
seminar. The principals’ secretary calls 4 families. Each family calls 4 other families
and so on. How many families will be notified during the VI round of calls?
Solution: Given: The secretary calls 4 families. Secretary
In each round, the number of calls is a power of 4.
I round: 4 calls = 4 1
II round: 16 calls = 4 × 4 = 4 2 I round: 4 calls
So, during the VI round, there will be
6
4 calls.
6
4 = 4 × 4 × 4 × 4 × 4 × 4 = 4,096 II round: 16 calls

EXERCISE 5.4

1. Rishi saves money to buy a saree for his mother. He puts ` 2 in a piggy bank on the first day and
each day he doubles the amount he saves from the day before. How much money does he save
on the tenth day?
2. In a school, the teacher gives a message to 4 students of her class and each of those students
convey the same message to other 4 students and so on. How many students will get the message
in the fifth round?
3. Pooja wants to predict the number of likes she will get on her blog. She received 3 likes on her
blog during the first week. If the number of likes triples every week, how many likes will she
recieve during the eighth week?
4. Riya tells a few Mathematics formulae to 3 friends on Sunday. The next day each of them tells
the same formulae to 3 more people. If this continues in the same manner, how many people will
know the formulae told by Riya on next Sunday.
5. The population of a certain town doubles every decade. If the population of the town in 2016
was 52,000, what was the population of the town in 1986?

AT A GLANCE

¾ If p is a non-zero rational number and n a natural number, then p × p × p × ... n times is equal
n
to p and is read as ‘p raised to the power n’.
n
¾ In exponential form p , p is called the base and n the exponent or the power.
¾ Numbers in exponential form obey certain laws. When a and b are non-zero rational numbers
and m and n are whole numbers, we have
n
m
m n
n
m
m
m
(a) a . a = a m + n (b) a ÷ a = a m – n (c) (a ) = a mn (d) a × b = (ab) m
1
0
m
–m
m
(e) a ÷ b =  a  m (f) a = 1 (g) a = m
 
 b  a
n
¾ Scientific notation or standard form of a number is of the form p × 10 , where p is a terminating
decimal greater than or equal to 1 and less than 10, i.e., 1 ≤ p < 10. Very large or very small
numbers can be conveniently written in this form.
MENTAL MATHS
1. Choose the correct answer.
3 2
(a) Which of the following is equivalent to (5 ) ?
9
6
5
(i) 5 (ii) 5 (iii) 5 (iv) (15) 2
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