Question

A colony of bacteria decreases in population by 10 percent each hour. The initial bacteria culture contained 250 spores. What exponential equation can be used to find the terms in the geometric sequence?(1 point)
Responses

b(x)=250(0.90)x−1
b left parenthesis x right parenthesis equals 250 left parenthesis 0.90 right parenthesis superscript x minus 1 baseline

b(x)=250(0.99)x−1
b left parenthesis x right parenthesis equals 250 left parenthesis 0.99 right parenthesis superscript x minus 1 baseline

b(x)=250−10(x−1)
b left parenthesis x right parenthesis equals 250 minus 10 left parenthesis x minus 1 right parenthesis

b(x)=250(0.10)x−1

Answer 1

To model the situation where a colony of bacteria decreases by 10 percent each hour, we can use the exponential decay formula. The initial population of bacteria is 250 spores, and since the population decreases by 10 percent, we retain 90 percent of the population each hour.

Thus, the equation for the population of bacteria after \( x \) hours can be expressed as:

\[ b(x) = 250(0.90)^x \]

However, since the options provided involve a slight variation where they use \( x - 1 \) in the exponent, we can rewrite the equation correctly as:

\[ b(x) = 250(0.90)^{x - 1} \]

So the correct option from the provided responses is:

**b(x) = 250(0.90)^(x - 1)**