A culture contains $680$ bacteria. After just $30$ Minutes, the count is $3250$ ) Find the number of bacteria after $3.5$ Hours
A) $2,380$
B) $38,651,370$
C) $7,140$
D) $19,000,000$
E) $11,375$

Question

Quizplus · Accepted Answer

The number of bacteria increases from 680 to 3250 in 30 minutes, indicating exponential growth. The formula for exponential growth is $P = P_0 e^{rt}$, where $P_0$ is the initial amount, $P$ is the amount after time $t$, $r$ is the rate of growth, and $t$ is the time in the same units used for the rate. Here, we can calculate the rate $r$ using the initial and final amounts over the first 30 minutes (0.5 hours). Then, we use this rate to find the number of bacteria after 3.5 hours. Given the options and the nature of exponential growth, the correct answer involves a significant increase from the initial count, leading to the selection of $38,651,370$ as the correct answer, which aligns with the exponential growth pattern.

A Culture Contains 680680680 Bacteria After Just 303030 Minutes, the Count Is 325032503250

A Culture Contains $680$ Bacteria After Just $30$ Minutes, the Count Is $3250$