A population of protozoa develops with a constant relative growth rate of 0.9973 per member per day. ?

dP/dt = 0.9973P

so, ∫ (1/P) dP = ∫ 0.9973 dt

=> lnP = 0.9973t + C

When t = 0, P = 6 so we have:

ln6 = C

Hence, lnP = 0.9973t + ln6

=> lnP - ln6 = 0.9973t

i.e. ln(P/6) = 0.9973t

=> P/6 = e^0.9973t

so, P(t) = 6e^0.9973t

Therefore, when t = 5 we have:

P(5) = 6e^(0.9973 x 5) = 879 people

:)>

P(5) = 879

RGR = (ln(P(t2)) - ln(P(t1))) / (t2 - t1)

P(t1), P(t2) populations on days t1 and t2, respectively

RGR - relative growth rate

RGR = 0.9973

P(0) = 6

P(5) = ?

t1 = 0

t2 = 5

ln(P(t2)) = RGR (t2 - t1) + ln(P(t1))

P(t2) = e^(RGR (t2 - t1) + ln(P(t1)))

P(t2) = P(t1) * e^(RGR *(t2 - t1))

P(5) = 6 * e^(0.9973*(5-0))

P(5) = 879

Edit:

Per days

P(0) = 6

P(1) = 16

P(2) = 44

P(3) = 120

P(4) = 324

P(5) = 879