BuyFind*launch*

4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 1.5, Problem 30E

(a)

To determine

**To Find:** The population of bacteria after 3 hours.

Expert Solution

There are 32,000 bacteria after 3 hours.

**Given:**

The initial population of bacteria is 500 and it gets double for every half hour.

**Calculation:**

Using the given initial population of bacteria
*t* as shown below,

Therefore,

Substitute

Therefore, there are 32,000 bacteria after 3 hours.

(b)

To determine

**To find:** The population of bacteria after *t* hours.

Expert Solution

There are
*t* hours.

**Given:**

The initial population of bacteria is 500 and it gets double for every half hour.

**Calculation:**

Using the given initial population of bacteria
*t* as shown below,

Therefore,

Substitute
*t* hours.

Therefore, there are
*t* hours.

(c)

To determine

**To Find:** The population of bacteria after 40 minutes.

Expert Solution

There are 1260 bacteria after 40 minutes.

**Given:**

The initial population of bacteria is 500 and it gets double for every half hour.

**Calculation:**

Using the given initial population of bacteria
*t* as shown below,

Therefore,

Convert the given time into hour as shown below,

40minutes =

Substitute

Therefore,. there are 1260 bacteria after 40 minutes.

(d)

To determine

**To estimate:** The time for the population

Expert Solution

**Graph:**

Use online graph calculator and draw the graph of the functions

From Figure 1, the curve intersects the line

That is, *t=*3.822 when

Therefore it takes 3.822 hours to reach to 100000 to the population.