Question
A professor is examining a new strain of bacteria. The amount of bacteria can be modeled by function s(n) = 20 ยท bn, where n is the number of hours and b is an unknown positive base.
Based on the model, there were initially _____
bacteria.
If b = 1.85, the hourly percent growth rate of the bacteria would be
_____%
Based on the model, there were initially _____
bacteria.
If b = 1.85, the hourly percent growth rate of the bacteria would be
_____%
Answers
Answered by
GPT-4o mini
To determine the initial amount of bacteria, we evaluate the function \( s(n) = 20 \cdot b^n \) at \( n = 0 \):
\[
s(0) = 20 \cdot b^0 = 20 \cdot 1 = 20
\]
Thus, there were initially **20** bacteria.
Next, to calculate the hourly percent growth rate of the bacteria when \( b = 1.85 \), we can use the formula for growth rate:
\[
\text{Growth Rate} = (b - 1) \times 100\%
\]
Substituting \( b = 1.85 \) into the formula:
\[
\text{Growth Rate} = (1.85 - 1) \times 100\% = 0.85 \times 100\% = 85\%
\]
Therefore, the hourly percent growth rate of the bacteria would be **85%**.
\[
s(0) = 20 \cdot b^0 = 20 \cdot 1 = 20
\]
Thus, there were initially **20** bacteria.
Next, to calculate the hourly percent growth rate of the bacteria when \( b = 1.85 \), we can use the formula for growth rate:
\[
\text{Growth Rate} = (b - 1) \times 100\%
\]
Substituting \( b = 1.85 \) into the formula:
\[
\text{Growth Rate} = (1.85 - 1) \times 100\% = 0.85 \times 100\% = 85\%
\]
Therefore, the hourly percent growth rate of the bacteria would be **85%**.
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