Function problem 2 by Dhaval Furia

Algebra Level pending

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 $_____$

(997)^{15} - 3

(997) 2^{14} + 3

(1003) 2^{15} - 3

(1003)^{15} + 6

1 solution

A Former Brilliant Member
Jun 12, 2020

Population after $n$ years is

$3(1+2+2^2+2^3+...+2^{n-1})+2^np=3(2^n-1)+2^np$ .

In this problem, $n=15,p=1000$ . So population in the beginning of $2034$ is $3( 2^{15}-1)+2^{15}\times 1000=(1000+3)\times 2^{15}-3=\boxed {(1003)\times 2^{15}-3}$ .

Function problem 2 by Dhaval Furia

1 solution

0 pending reports