A bacterial culture grows with a constant relative growth rate. Its numbers are

Question

A bacterial culture grows with a constant relative growth rate. Its numbers are 600 bacteria after 4 hours and 1, 800 bacteria after 5 hours. (i) What was the initial population of the culture? P_0 = bacteria. Round the answer to the nearest integer. (ii) Calculate the number of bacteria after 6 hours. Round the answer to the nearest integer. (iii) What is the growth rate of the population after 6 hours? Round the answer to the nearest integer. (iv) How much time will it take for their numbers to reach 2, 368.933223 bacteria? Round the answer to the nearest integer.

Explanation / Answer

P(t) = P(0) k^t

(OR P(t) = P(0) . exp[ln(k) . t] . )

P(4) = P(0) k^4 = 600
P(5) = P(0) k^5 = 1800

P(5)/P(4) = P(0) k^5 / P(0) k^4 == 1800/600 , so k = 3

i) P(0) = 600/k^4 = 600/3^4 ==> 600/ 81 ==> 7.40740741
P(t) = 7.40740741 *3^(t)

ii) P(6) = 7.40740741 * 3^(6) ==> 5400

d) P(t) = 7.40740741 * exp[ln(3) . t]
P'(t) = ln(3) P(t)

P'(6) = ln(3) P(6)
P'(6) = ln(3)*  7.40740741 * 3^(6) = 5932.50636

e) P(t) = 7.40740741 * 3^(t) = 2,368.933223

3^(t)= 2,368.933223 / 7.40740741

ln( 3^t) = ln ( 2,368.933223 / 7.40740741 )
t= ln(2,368.933223 / 7.40740741) / ln(3)

t = 5.25000 hrs

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.