Question

Bacteria culture A culture of the bacterium Rhodobacter sphaeroids initially had 30 bacteria and t hours later increases at a rate of 2e2t 1 bacteria per hour. Find the population size after four hours

Answer 1

Complete Question

Bacteria culture A culture of the bacterium Rhodobacter sphaeroids initially had 30 bacteria and t hours later increases at a rate of 2e^2t 1 bacteria per hour. Find the population size after four hours

Answer:

3010

Step-by-step explanation:

We were given the rate: 2e^2t

Step 1

We would integrate

P = Population

dP/dt = 2e^2t

dP =( 2e^2t) dt

∫dP = ∫ 2e^2t dt

P(t) = (2e^2t)/2 + C

P(t) = e^2t + C

Step 2

We solve for C

The culture initially has 30 bacteria

When t = 0

P(0) = 30

P(0) = e^2t + C

30 = e^2× 0 + C

30 = 1 + C

C = 30 - 1

C = 29

Step 3

Find the population size after four hours

t = 4, C = 29

P(t) = e^2t + C

P(4) = e^2 × 4 + 29

P(4) = e^8 + 29

P(4) = 3009.957987

Approximately = 3010 bacteria