Question

type the correct answer in each box. use numerals instead of words. if necessary, use / for the fraction bar(s)
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 initially bacteria.
if b = 1.85, the hourly percent growth rate of the bacteria would be %

Explanation:

Step1: Find initial amount

When \(n = 0\), \(s(0)=20\cdot b^{0}\). Since \(b^{0}=1\) for any non - zero \(b\), \(s(0)=20\).

Step2: Calculate growth rate

The general form of an exponential growth function is \(y = a(1 + r)^{t}\), where \(r\) is the growth rate. Given \(s(n)=20\cdot b^{n}\) and \(b = 1.85\), we can write it as \(s(n)=20\cdot(1 + 0.85)^{n}\). So the growth rate \(r=0.85\) or \(85\%\).

Answer:

20; 85