Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

Question

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.

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 find the initial amount of bacteria, we evaluate the function \( s(n) \) at \( n = 0 \):

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

Thus, there were initially 20 bacteria.

Next, to find the hourly percent growth rate when \( b = 1.85 \), we can calculate the growth rate using the formula for percent growth rate:

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

Substituting \( b = 1.85 \):

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

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

In summary:

Initial amount of bacteria: 20
Hourly percent growth rate: 85