Question

A certain microbe, growing at a rate proportional to its size, doubles its population every 10 hours. After 13 hours the total population has mass 560 grams. What was the initial mass? (Round your answer to 3 decimal places.) initial mass = grams Submit Answer Tries 0/3

Answer 1

Given that Growing rate is proportional to its size. Let the mass is P (t) at time at hos So of PCL) -) KP (Kn Amy Coutant) - dp = kt ) In P = atte =) poeta cent. (As ees Anothe S abitary Const) In p =kt te At t=o, p(o)=c hitial mas And after 10 hos , mass doubls, So P(+) = 2e - lelor - af : 10k = lna - Ik= 0.11n2 = 0.0693. Aftere 13 hrs , P(13) = 560 gram 7) cée 560 =) ( 0.0693 x 12 560 227.43 - 0.0699813 е 227 Tinitial mass = c = 2274