Question

Marcus is doing a science experiment in which he measures the rate at which bacteria multiply. Every 15 seconds, the bacteria double in number. If there are 10 bacteria now, how many will there be in 2 minutes?

Answer 1

Since there are 10 bacteria, the amount of bacteria after 2 minutes is 2560 bacteria

To answer the question, we need to know what rate is

What is rate?

A rate is the amount per unit time of a quantity.

Let A₀ = initial amount of bacteria.

Given that the amount of bacteria doubles every 15 seconds, we have that the amount of bacteria left is

A = 2ⁿA₀ where

• n = number of 15 seconds that have passed = t/15 where
• t = time passed.

Given that

• A₀ = 10 and
• t = 2 min = 2 × 60 s = 120 s.
• So, n = t/15 = 120/15 = 8

Amount of bacteria after 2 minutes

So, substituting the values of the variables into the equation, we have

A = 2ⁿA₀

A = 2⁸ × 10

A = 256 × 10

A = 2560 bacteria

So, the amount of bacteria after 2 minutes is 2560 bacteria

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