Question

a researcher is testing how bacterial cells react to different environments. she placed a petri dish that initially had 32,000 bacterial cells in a vacuum chamber. one hour after being placed in the vacuum chamber, the number of cells in the petri dish had halved. another hour later, the number of cells had again halved. the researcher creates an equation that models this pattern and can be solved to find the number of cells, y, in the dish x hours after being placed in the vacuum chamber. plot the y - intercept of the equation and the points representing the solutions for the first three hours after the cells were placed in the vacuum chamber.

Explanation:

Step1: Find the y - intercept

The y - intercept occurs when \(x = 0\). Initially, there are 32000 bacterial cells. So the point is \((0,32000)\)

Step2: Find the number of cells after \(x = 1\) hour

The number of cells halves after 1 hour. So \(y=32000\times\frac{1}{2}=16000\). The point is \((1,16000)\)

Step3: Find the number of cells after \(x = 2\) hours

The number of cells halves again. So \(y = 16000\times\frac{1}{2}=8000\). The point is \((2,8000)\)

Step4: Find the number of cells after \(x = 3\) hours

The number of cells halves once more. So \(y=8000\times\frac{1}{2} = 4000\). The point is \((3,4000)\)

Answer:

Plot the points \((0,32000)\), \((1,16000)\), \((2,8000)\) and \((3,4000)\) on the graph.