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Question

A professor is examining a new strain of bacteria. The amount of bacteria can be modeled by function s(n)=20*b^n where n is the number of hours and b is an unknown positive base.
Based on the model, there were initiallay __________ bacteria.

If b = 1.85, the hourly percent growth rate of the bacteria would be______%.

Answer 1

To find the initial amount of bacteria, we look at the function \( s(n) = 20 \cdot b^n \). When \( n = 0 \), this gives us the initial amount:

\[ s(0) = 20 \cdot b^0 = 20 \cdot 1 = 20 \]

So, there were initially 20 bacteria.

Next, to find the hourly percent growth rate when \( b = 1.85 \), we use the formula for percent growth rate, which is given by:

\[ \text{Percent Growth Rate} = (b - 1) \times 100% \]

Substituting \( b = 1.85 \):

\[ \text{Percent Growth Rate} = (1.85 - 1) \times 100% = 0.85 \times 100% = 85% \]

Thus, the hourly percent growth rate of the bacteria would be 85%.

In summary:

• Initially: 20
• Hourly percent growth rate: 85