9) Find the area of the triangle. *

As we can see it's right angle triangle

so:

answer:  

let x represents the number of hours and y represents the total number of bacteria after x hours.

then the function that shows the given situation,

where a is the initial number of bacteria b is the growth factor.

according to the question,

the experiment is started with 800 bacteria cells and growth rate of the bacteria cells was 3.2%.

thus, a = 800 and b = 1 + 3.2% = 1+.032 = 1.032 (because, growth factor = 1+ growth rate)

⇒   the function that shows the given situation,

which is an increasing exponential function.

that having y-intercept = (0, 800)

but does not have x-intercept.

end behavior:

since, 3.2 > 1

therefore, end behavior of the function is,

as ,  

as ,    

thus, from the above information, we can plot the graph of the given situation.

now, for x = 35

thus, the point that represents the projected bacteria population 35 h from the time henrietta started the experiment = (35, 2409.236)