Trigonometry (11th Edition)
11th Edition
ISBN: 9780134217437
Author: Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher: PEARSON
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![**Problem: Bacterial Growth**
A type of bacteria doubles every 8 hours. If you started with 12 spores in a Petri dish, how many spores would you have after 48 hours?
**Fill in the BLANK**
After 48 hours, there would be ______________ spores.
**Solution Explanation:**
To determine the number of spores after 48 hours, consider the doubling period. The spores double every 8 hours.
1. Calculate the number of doubling periods in 48 hours:
\[
\frac{48 \text{ hours}}{8 \text{ hours per doubling}} = 6 \text{ doublings}
\]
2. Start with 12 spores and double the amount 6 times:
\[
\text{After 1 doubling: } 12 \times 2 = 24
\]
\[
\text{After 2 doublings: } 24 \times 2 = 48
\]
\[
\text{After 3 doublings: } 48 \times 2 = 96
\]
\[
\text{After 4 doublings: } 96 \times 2 = 192
\]
\[
\text{After 5 doublings: } 192 \times 2 = 384
\]
\[
\text{After 6 doublings: } 384 \times 2 = 768
\]
Therefore, after 48 hours, there would be **768 spores**.](https://content.bartleby.com/qna-images/question/1c3f0c16-4bc2-4005-8b34-f5a8ba23d8d8/aa269848-e43f-4267-946d-9947b41b02ef/flrqt4a_processed.jpeg)
Transcribed Image Text:**Problem: Bacterial Growth**
A type of bacteria doubles every 8 hours. If you started with 12 spores in a Petri dish, how many spores would you have after 48 hours?
**Fill in the BLANK**
After 48 hours, there would be ______________ spores.
**Solution Explanation:**
To determine the number of spores after 48 hours, consider the doubling period. The spores double every 8 hours.
1. Calculate the number of doubling periods in 48 hours:
\[
\frac{48 \text{ hours}}{8 \text{ hours per doubling}} = 6 \text{ doublings}
\]
2. Start with 12 spores and double the amount 6 times:
\[
\text{After 1 doubling: } 12 \times 2 = 24
\]
\[
\text{After 2 doublings: } 24 \times 2 = 48
\]
\[
\text{After 3 doublings: } 48 \times 2 = 96
\]
\[
\text{After 4 doublings: } 96 \times 2 = 192
\]
\[
\text{After 5 doublings: } 192 \times 2 = 384
\]
\[
\text{After 6 doublings: } 384 \times 2 = 768
\]
Therefore, after 48 hours, there would be **768 spores**.
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