Question 9.

If the population of a town is p in the beginning of any year then it becomes 3 + 2p in the beginning of the next year. If the population in the beginning of 2019 is 1000, then the population in the beginning of 2034 will be

A
(1003)15+6(1003)^{15} + 6
B
(997)153(997)^{15} - 3
C
(997)214+3(997)2^{14} + 3
D
(1003)2153(1003)2^{15} - 3

Question Explanation

Text Explanation

The population of town at the beginning of 1st year = p

The population of town at the beginning of 2nd year = 3+2p

The population of town at the beginning of 3rd year = 2(3+2p)+3 = 2*2p+2*3+3 =4p+3(1+2)

The population of town at the beginning of 4th year = 2(2*2p+2*3+3)+3 = 8p+3(1+2+4)

Similarly population at the beginning of the nth year = 2n12^{n-1}p+3(2n112^{n-1}-1) = 2n1(p+3)2^{n-1}\left(p+3\right)-3 

The population in the beginning of 2019 is 1000, then the population in the beginning of 2034 will be (220342019)(1000+3)(2^{2034-2019})\left(1000+3\right)-3 = 215(1003)2^{15}\left(1003\right)-3

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