**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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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

Trigonometry (11th Edition)

11th Edition

ISBN:9780134217437

Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Chapter1: Trigonometric Functions

Section: Chapter Questions

Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.

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Question

**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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