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:

The population of bacteria after 6 days is 2,313.06

Step-by-step explanation:

Given as :

The initial population of bacteria = i = 1,000 bacteria

The growth rate of bacteria per day = 15%

Let The population of bacteria after 6 days = f

The time period of growth = 6 days

Now, According to question

The population of bacteria after 6 days = initial population × $(1+\dfrac{\textrm rate}{100})^{\textrm time}$

Or, f = i × $(1+\dfrac{\textrm r}{100})^{\textrm t}$

Or, f = 1000 × $(1+\dfrac{\textrm 15}{100})^{\textrm 6}$

Or, f = 1000 × $(1.15)^{6}$

Or, f = 1000 × 2.31306

∴  f = 2,313.06

So,The population of bacteria after 6 days = f = 2,313.06

Hence,The population of bacteria after 6 days is 2,313.06  Answer