Grade 12th passDifferential Calculus
Please solve the questions no 18 and 19. I sent a image.
2 Answers
Chandan
I know for 19Let current population be pdp/dt=kpK= proportionality constantWe solving we getP=e^ktAs population doubles in 50 days2=e^50kK=ln2/50For triple population3=e^tkPut the value of k you will get the answerPlease feel free to ask any doubt in the solution I will be happy to help
Khimraj
Q 19.
Let the population at time t= 0 days is p =po
then after 50 days population become 2po.
According to question
dp/dt = kp
where k is proportionality constant
dp/p = kdt
logp = kt + c
at t= 0 p = po
logpo = c
So equation become
logp = kt + logpo
log(p/po) = kt
at t = 50, p = 2po
log2 = 50k
so k = (log2)/50
so equation become
log(p/po) = ((log2)/50)t
time at which population become triple(p = 3po)
log3 = ((log2)/50)t
so t = 50[(log3)/(log2)].
Hope it clears. If you like answer then please approve it.
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