Chapter 5: Q. 125 (page 288)

The bacteria in a $4$ -liter container double every minute. After $60$ minutes the container is full. How long did it take to fill half the container?

Short Answer

Expert verified

It will take $59 m i n u t e s$ to fill half the container.

Step by step solution

Step 1. Given information.

Consider the given question,

It takes $60$ minutes to fill the full container.

Assume $y = a e^{b t}$ to be the formula that considers the growth of bacteria.

As the bacteria doubles every minute, then,

$2 a = a e^{b} b = \ln (2) b = 0.693$

Step 2. Substitute the values in the formula.

Substitute $t = 60, b = 0.693$ in the formula,

$4 = a e^{0.693 \times 60} a = 3.469 \times 10^{- 18}$

Assume the container is half filed or it is $2$ liters. Then,

$2 = 3.469 \times 10^{- 18} e^{0.693 \times t} t = 59 m i n u t e s$

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The bacteria in a $4$ -liter container double every minute. After $60$ minutes the container is full. How long did it take to fill half the container?

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Substitute the values in the formula.

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The bacteria in a 4-liter container double every minute. After 60minutes the container is full. How long did it take to fill half the container?

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Substitute the values in the formula.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Applied Mathematics

Theoretical and Mathematical Physics

Pure Maths

Discrete Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

The bacteria in a $4$ -liter container double every minute. After $60$ minutes the container is full. How long did it take to fill half the container?