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)

Question

Responses

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
b left parenthesis x right parenthesis equals 250 left parenthesis 0.10 right parenthesis superscript x minus 1 baseline

b(x)=250(0.90)x−1

Answer 1

To determine the correct exponential equation that represents the decrease in the bacteria population, we start with the initial population of 250 spores and recognize that the population decreases by 10% each hour.

A 10% decrease means that 90% of the population remains each hour. This can be represented mathematically as:

• The remaining population after \( x \) hours is given by:

\[ b(x) = 250 \times (1 - 0.10)^x \]

Since \( 1 - 0.10 = 0.90 \), we have:

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

However, the options provided use \( x - 1 \) instead of \( x \), which typically indicates that they are showing values starting at \( x = 1 \) instead of \( x = 0 \).

By adjusting the function to account for that, we can rewrite it with \( x - 1 \):

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

Thus, the correct option from the choices given is:

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

So the correct response is:

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