A scientist has started a bacteria culture with 1,000 cells. The cells will double every hour. 1. Write the sequence that represents the number of bacteria cells over the first 4 hours. 2. What is the common ratio of the sequence that represents the growth of the bacteria cells?3. How many bacteria cells will there be after 7 hours?4. During what hour will the number of bacteria cells exceed one million?

Question

Mathematics

Clayton Hardy

26 June, 03:40

A scientist has started a bacteria culture with 1,000 cells. The cells will double every hour. 1. Write the sequence that represents the number of bacteria cells over the first 4 hours. 2. What is the common ratio of the sequence that represents the growth of the bacteria cells?3. How many bacteria cells will there be after 7 hours?4. During what hour will the number of bacteria cells exceed one million?

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Answers (1)

Know the Answer?

Alvaro Pierce · Answer 1

See below in bold.

Step-by-step explanation:

1. The sequence is 1000, 2000, 4000, 8000.

2. The common ratio is 2000/1000 = 2.

3. Number of bacteria after 7 hours is 1000 (2) ^ (7 - 1)

= 64,000.

4. 1000 (2) ^ (x-1) > 1,000,000

2^x-1 > 1000

x - 1 log 2 > log 10

x - 1 > 9.96

x > 10.96

During the 11th hour.