Question

A growth medium is inoculated with 1,000 bacteria, which grow at a rate of 15% each day. What is the population of the culture 6 days after inoculation?

Answer 1

Answer:

2313

Step-by-step explanation:

A = P(1+r)^t

where A is the final amount, P is the initial amount, r is the rate, and t is time.

Here, P = 1000, r = 0.15, and t = 6.

A = 1000(1.15)^6

A ≈ 2313

Answer 2

Number of bacteria after 6 days is 2313

Step-by-step explanation:

Population after n days is given by

              $P_n=P_0(1+r)^n$

Initial population, P₀ = 1000

Increase rate, r = 15 % = 0.15

Number of days, n = 6

Substituting

             $P_n=P_0(1+r)^n\\\\P_6=1000(1+0.15)^6\\\\P_6=1000(1.15)^6\\\\P_6=1000\times 2.313\\\\P_6=2313$

Number of bacteria after 6 days = 2313