1. henrietta did an experiment. she started out with 800 bacteria cells. she found that the growth rate of the bacteria cells was 3.2%. sketch the graph that represents the situation. label the y-intercept and the point that represents the projected bacteria population 35 h from the time henrietta started the experiment.

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)

the graph in the attached figure

step-by-step explanation:

we have

using a graphing tool

the graph in the attached figure

the roots are ( x-intercepts) x=-0.5,x=1,x=3

the y-intercept is the point (0,3)

step-by-step explanation:

for the free