Question

Exponential Function:

Activity: Bacterial population

A population of bacterium in laboratory conditions grows every 20 minutes in 10% the number of specimens. At the beginning of the observation, at 8:00 AM, the population had approximately 3,000,000 individuals:

1. Complete the following attached table (table below) as requested by completing each of the blank boxes.

2. What is the approximate population of bacterium at 10:00 AM?

3. Write the function in power form, indicating which is the dependent and independent variable.

4. Using the function found, determine the bacterial population five hours after the start of the observation.

Answer 1

See below

Explanation:

Given

• Initial population at 8:00 AM
• 3000000
• Growth rate = 10% = 1.1 times per 20 min

Solution

1. Table

Note. I am not sure what are the last 3 rows. Just added next 3 terms.

• 8:00 ≡ G(0) ≡ 3000000 ≡ 3000000
• 8:20 ≡ G(1) ≡ 3000000 *1.1 ≡ 3300000
• 8:40 ≡ G(2) ≡ 3000000 *1.1^2 ≡ 3630000
• 9:00 ≡ G(3) ≡ 3000000 *1.1^3 ≡ 3993000
• 9:20 ≡ G(4) ≡ 3000000 *1.1^4 ≡ 4392300

2. Population at 10:00

• Time passed since 8:00 is 2 hours = 2*3*20 min = 6* 20 min
• Population = 3000000*1.1^6 = 5314683

3. Function to reflect the population growth

• G(x) = 3000000*1.1^x
• G(x) - is dependent variable, population of bacteria
• x - is independent variable, time increment of 20 min

4. Population after 5 hours

• 5 hours = 5*3*20 min = 15*20 min
• G(15) = 3000000*1.1^15 ≈ 12531745