5

Having completed your first few tasks. you move now to a portion of the lab where important bacteria are being grown. Based on the data collected, you have determined that the population of this bacteria in the range measured can be modeled as AB] = 2050.11)? where t is given in days. To the nearest whole number, what will the bacteria population be after 5 days? The bacteria population will be Explain, in your own words and with your own work, how you arrived at this result. Be sure to explain using appropriate mathematical concepts to support your coworkers and supervisor. After checking the bacteria population that was assigned to you, you remember that lCasey had asked you to provide some analysis for the growth of their bacteria that they are hoping will speed up the production of an important material. Casey has asked you to take the function that models the population size, nd the domain, range, and minimum value, and then plot the results. Casey specifically asked for these values related to the function that ts the data. They also wanted the input value of zero to represent the date that the data was collected. This makes negative input values represent previous days and positive values represent future predictions. After careful analysis, you determine that the function modeling the bacteria population is f(:.:) = 5(2)\": + 7. You next carefully find the domain and range in interval notation. To enter {)0 when in text mode, type innity. To enter 00 when in symbol mode, choose the 00 symbol. Domain: IQ Range: IQ Minimum Value y = @ E Casey has also asked for a graph of this function. Which graph do you sketch in your notebook? 1C| 8 6 4 Explain, in your own words and with your own work, how you arrived at this result (including the graph). Be sure to explain using appropriate mathematical concepts to support your coworkers and supervisor. After analyzing Casey's bacteria population. you see a note that you had made for yourself that Casey wanted this information updated on their computer. You walk over to lCasey's computer and see a note taped to the monitor with a password reminder. While you are glad to have this information, you can only wonder what the Information Security team would think about this practice. You review Casey's note and enter the password 8.8 2 Password: Rewrite e h as an equivalent logarithmic equation. Enclose arguments of functions in parentheses and include a multiplication sign between terms. For example, 0 * log (it). . \".i F'F'! ~ ,15 state] f JF 3:; ac (.1 it [If '9' (is: Explain, in your own words and with your own work, how you arrived at this result. Be sure to explain using appropriate mathematical concepts to support your coworkers and supervisor. "Which of the following graphs best represents the graph of g (at)? Explain, in your own words and with your own work, how you arrived at this result (including the graph). Be sure to explain using appropriate mathematical concepts to support your coworkers and supervisor. While on Casey's computer, you notice that a model for a recent experiment is completed. The model gives the temperature (7") as a function of time (t) as given below. As before, a time of t = Orepresents the time of data collection, with negative values representing earlier times. Knowing Casey, they will want to know the domain, range, and other information about the model. You review the model and provide the information that Casey will request. T(t) = In (3t + 24) + 1.4 Enter the domain in interval notation. To enter co, type infinity. The vertical asymptote is t = As t approaches the vertical asymptote, T(t) -+ As t approaches co, T(t) + G G. Which of the following graphs best represents the graph of g (a)? O O