Strain of Bacteria

[umaa]

A strain of bacteria multiples such that the ratio of its population in any two consecutive minutes in constant,
If the bacteria grows from a population of 5 million to a population of 40 million in one hour, by what factor does the population increase every 10 minutes?

OA is sqrroot 2

[thephoenix]

basically its a GP
start =5*10^6=say x0
after 2min its x0*r(say r as a constant factor)
similarly for 10th min its x0*r^5 we are asked what is r^5and for 6oTh min its x0*r^30=40*10^6

now we know x0=5*10^6

therefore for 60th min x0*r^30=40*10^6
or r^30=40/5=8
which is same as r^5)^6=2^3
solving r^5=sqrroot 2

hence ans is sqrroot2

[Birgit Anne]

I understand it until the point r^30=8, but I cannot follow your last two steps.

Can anyone please explain that to me?

[thephoenix]

I understand it until the point r^30=8, but I cannot follow your last two steps.

Can anyone please explain that to me?

r^30=8
(r)^(5*6)=2^3
taking sixth root both side
r^5=2^(3/6)
r^5=2^(1/2)=sqrt2
hence r^5=sqrt2

and every tenth minute its inc by factor of r^5 and hence sqrt2

HTH

[adam15]

we know that the ratio between two successive minute is constant thus
let t1 the first minute and t2 second minute...t60
thus
t1/t2=t2/t3=t3/t4=...=t59/t60=r
multiple all terms
t1/t2*t2/t3....*t58/t59*t59/t60=r*r....*r (6o times)
thus
t1/t60=r^60
we know that t1 correspond to 5, and t60 correspond to 40 thus
5/40=2^3
thus r^60=2^3
thus r=2^(1/20)
after 10 minute we will have

r^10=2^(1/2)= square root of 2

[Birgit Anne]

Thank you both!