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,

9 A . 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 \geq 0} {y ∣ y \geq 300}

Showing Our Work

Drawing the function

To draw

p = 300 (2.7)^{0.02 \cdot t},

we need to change the variables.

p = 300 (2.7)^{0.02 t} \Leftrightarrow y = 300 (2.7)^{0.02 x}

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 $2 nd,$ $TRACE,$ 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 $300 .$

Exercise