A professor is examining a new strain of bacteria. The amount of bacteria can be modeled by function s(n) = 20 · bn, where n is the number of hours and b is an unknown positive base.

Question

Based on the model, there were initially _____
bacteria.

If b = 1.85, the hourly percent growth rate of the bacteria would be
_____%

Answer 1

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%.