Question

15 (1).pdf x SIGNMENT%201-MATH215%20(1).pdf V. A. In a certain culture of bacteria, the rate of increase is proportional to the number of present (a) if it is found that the number doubles in 5 hours, how many may be expected at the end of 10 hours? (b) if there are 104 at the end of 4 hours and 4.104 at the end of 6 hours, how many were there in the beginning?

is the calculation

Answer 1

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PCP)the size of the bacteria population of time t de KP de de kat Р Integral Clip]dt - Integral (k]dt Inlpl kt+ci IPI = e ekt til ikt kt Ceki kt P= ce PO) Po Klo) Ce Po = Po PCE Pock it 0 P(5) = 20 bo ek(s) _ 200 اکے in skinz skine in 2 5k = lna (11.22/5

P(t) = Poe [In 2)/5] PCE) Po Cehajt15 Plt) Po 227715 Pcela Po let's) PCIO:) Po (205) Priol Po (2²) PCIO): 480 Plt) = Poétt PCU) 4 10 ku) Po ek 4 10 Po 10 luk Ux10 P(6) k(6) 4110 Por UXIO Gic uxiol 4k hela [. . Po : id lect] fuxio ) euk 4.6k GE elk sol 2 L

in 2k iny akne lny 2k = lnu. K= (114)/2 PLE) = Poe [(n)/2]t th Pct) =:Pole iny] PCD) = Po (4 1412 Plt). Put P(u) = 10 lol Poi (u/2) = 10 Pou? = col 104 Po U2 Po = 625