Question

A bacteria population starts with 100 bacteria. It triples every hour. Write an exponential equation to represent the population (P) after 't' hours. Calculate the population after 5 hours.

Answer 1

• 24,300

Explanation:

To represent the population (P) of bacteria after 't' hours, We can use the exponential equation:

`\: \longrightarrow \: \: \large \boxed{ \sf{\[P(t) = P_0 \cdot 3^t\]}}`

Where:

• (P(t)) is the population after 't' hours.
• 
  `( \sf{P_0)}` is the initial population, which is 100 bacteria in this case.
• 't' is the number of hours.

↪ Now, to calculate the population after 5 hours:

`➟ \: \: \: \sf{\[P(5) = 100 \cdot 3^5\]</p><p>}`

`</p><p>➟ \: \: \: \sf{\[P(5) = 100 \cdot 243\]</p><p>}`

`➟ \: \: \: \sf{\[P(5) = 24,300\]}`

So, the population of bacteria after 5 hours will be 24,300.