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Ryan wants to describe the translation shown on the grid below.

On a coordinate plane, triangle X Y Z is shifted 1 unit to the left and 3 units up to form triangle X prime Y prime Z prime.

Ryan uses the following steps to describe the translation.

Step 1 Identify the pre-image and the image:
The pre-image is triangle XYZ, and the image is X prime Y prime Z prime.

Step 2
Identify the number of units that each point moves horizontally:
Each point moves one unit left.

Step 3
Identify the number of units that each point moves vertically:
Each point moves three units down.

Step 4
The translation is one unit left and three units down.

In which step did Ryan make the first error?
Step 1
Step 2
Step 3
Step 4

The biologist has a second culture to examine. she knows that the population of the culture doubles every 15 minutes. after 1 hour and 15 minutes, her assistant found that 80,000 bacteria were present. a) what was the size of the initial population? b) predict the size of the culture at t=3 hours. what was the size of the population at 40 minutes? explain and justify your answers. c) create a graph of the population as a function of time. find an equation that can be used to predict the size of the population at any time t. d) examine the rate at which the bacteria culture is growing. how fast is the culture growing after 1 hour? after 1.5 hours? after 2 hours? use a time interval of h = 0.01 hours to estimate these rates. interpret these rates in terms of the context of the problem situation. how do these three rates compare?