Question

The bacteria in a Petri dish culture are self-duplicating at a rapid pace. The relationship between the elapsed time ttt, in minutes, and the number of bacteria, B(t)B(t)B, left parenthesis, t, right parenthesis, in the Petri dish is modeled by the following function. B(t)=10⋅2t12 How many bacteria will make up the culture after 120120120 minutes? Round your answer, if necessary, to the nearest hundredth.

Answer 1

4,09,600 bacteria will make up the culture after 120 minutes .

Step-by-step explanation:

Here we have , The bacteria in a Petri dish culture are self-duplicating at a rapid pace. The relationship between the elapsed time t, in minutes, and the number of bacteria, B(t)B(t)B, left parenthesis, t, right parenthesis, in the Petri dish is modeled by the following function. B(t)=10⋅2t12 . We need to find How many bacteria will make up the culture after 120120120 minutes . Let's find out:

We have the following equation to determine the number of bacteria made up in time t as

⇒ $B(t) = 100(2)^{\frac{t}{10}$

According to question given value of t is , 120 min so :

⇒ $B(t) = 100(2)^{\frac{120}{10}$

⇒ $B(t) = 100(2)^{12}$

⇒ $B(t) = 100(4096)$

⇒ $B(t) =4,09,600$

Therefore , 4,09,600 bacteria will make up the culture after 120 minutes .

Answer 2

Answer:

10,240  bacteria in the culture after 120 minutes.

Step-by-step explanation: