The population of cattle in a farm increases | vedclass

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Question

(b)

Given,

Population in year $2010, 2011$ and $2013$ were $39,60$ and $123$ respectively.

According to problems,

The population of cattle

Vedclass · Accepted Answer

$84$

Vedclass · Answer

(b)

Given,

Population in year $2010, 2011$ and $2013$ were $39,60$ and $123$ respectively.

According to problems,

The population of cattle in farm increases such that difference between in year $n+2$ and that in year $n$ is proportional to the year $n+1$

$\because \quad(n+2)-(n)=k(n+1)$

$\because$ Let population in year $2012=x$


	
		
			$Year$
			$Population$
		
		
			$2010$
			$39$
		
		
			$2011$
			$60$
		
		
			$2012$
			$x$
		
		
			$2013$
			$123$
		
	


From Eqs.$(i)$ and $(ii)$, we get

$\frac{x-39}{60}=\frac{123-60}{x}$

$\Rightarrow x^2-39 x-3780=0$

$\Rightarrow (x-84)(x+40)=0$

$	herefore x=84$

The population of cattle in a farm increases so that the difference between the population in year $n+2$ and that in year $n$ is proportional to the population in year $n+1$. If the populations in years $2010, 2011$ and $2013$ were $39,60$ and $123$,respectively, then the population in $2012$ was

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