a The function p models the growth of bacteria population.
p=300(2.7)0.02t
Here, t is the number of hours. Since t=0 corresponds to 9:00AM, the elapsed time is 2 hours until 11:00AM. Hence, we need to substitute 2 for t in the function.
b Let's see how the graph looks like in the graphing calculator.
We see that the p-intercept is 300. It represents the number of bacteria in the culture at t=0, or 9A.M. Since t represents time, a reasonable domain is all non-negative real numbers. At t=0, the number of bacteria is 300, so a reasonable range is all real numbers greater than or equal to 300.
Domain:Range:{t∣t≥0}{y∣y≥300}
Showing Our Work
Drawing the function
To draw p=300(2.7)0.02⋅t, we need to change the variables.
p=300(2.7)0.02t⇔y=300(2.7)0.02x
Push the button Y= and enter the equation in the first row.
Push GRAPH and the calculator will draw the equations. For this function to be visible on the screen, re-size the standard window by pushing the WINDOW button. Change the settings to a more appropriate size and then push GRAPH.
To find the y-intercept, we can use the trace feature to find the value of the function at x=0. This can be done by pressing 2nd,TRACE, and choosing the value option. Finally, enter 0 and it will give you the y-intercept.
Since y and p represent the same thing, the p-intercept is 300.
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