Question

jim is growing a bacterial culture in a dish for a science project. the graph shows the population of the culture in the dish for the first three hours. which statement about the graph is true? jim starts with 200 bacteria, and the population of bacteria doubles every hour. jim starts with 200 bacteria, and the population of bacteria triples every hour. jim starts with 100 bacteria, and the population of bacteria doubles every hour. jim starts with 100 bacteria, and the population of bacteria triples every hour.

Explanation:

Step1: Determine the initial population

When \(x = 0\) (initial time), from the graph, \(y=100\). So Jim starts with 100 bacteria.

Step2: Check the growth factor

At \(x = 1\), \(y\approx300\); at \(x = 2\), \(y\approx900\).
We know that if the initial population is \(P_0 = 100\), and the population at time \(x\) is \(P(x)=P_0\times r^x\).
When \(x = 1\), \(P(1)=100\times r\). Since \(P(1) = 300\), then \(r = 3\).

Answer:

Jim starts with 100 bacteria, and the population of bacteria triples every hour.