Exponential Growth (WORD PROBLEM: bacterial growth)

[plur222]

E.coli is a bacterium that reproduces by dividing. Each bacterium splits into two parts every half hour.
This is an example of exponential growth and can be modeled as follows:

Assuming that none of the bacteria die,

P(t)= P x 2^2t where P is the initial population and t is time in hours

According to this function, it is obvious that a small number of bacteria in the gut of humans can trigger a large infection in a short period of time. Assume an initial infection of 100 bacteria (P=100).

Begin by sketching the exponential growth function, on the time interval [0,3] hours. Use the method of transformations. Clearly show all steps in the graphing procedure. Identify the asymptote and the exact coordinates of two points on the graph. Label your axes appropriately.

Then rewrite this function in logarithmic form.

How long until the bacteria population reaches 10,000?

In trying to get points I have got (3,64) (2,16) (1,4) (0,1) (-1,0.50) (-2,0.25) is this right?

I don't understand what the time interval [0,3] means ... do I start the graph at (0,3) or are the points to be 3 points apart?

I just don't get word problems?!?!?!

 

[Deleted member 4993]

Re: Exponential Growth (WORD PROBLEM)

E.coli is a bacterium that reproduces by dividing. Each bacterium splits into two parts every half hour.
This is an example of exponential growth and can be modeled as follows:

Assuming that none of the bacteria die,

P(t)= P x 2^2t where P is the initial population and t is time in hours

According to this function, it is obvious that a small number of bacteria in the gut of humans can trigger a large infection in a short period of time. Assume an initial infection of 100 bacteria (P=100).

Begin by sketching the exponential growth function, on the time interval [0,3] hours. Use the method of transformations. Clearly show all steps in the graphing procedure. Identify the asymptote and the exact coordinates of two points on the graph. Label your axes appropriately.

Then rewrite this function in logarithmic form.

How long until the bacteria population reaches 10,000?

In trying to get points I have got (3,64) (2,16) (1,4) (0,1) (-1,0.50) (-2,0.25) is this right? ....No

The bacteria colony is growing!!

So if you start with 100 bacteria (t = 0) , how could you end-up with less (64) after 1 hour?



I don't understand what the time interval [0,3] means

That is the range of function - you start at t= 0 and end at t= 3 (with in between values like t = 0.1, 0.5, 1, 1,5, 2, 2.5, ...)

... do I start the graph at (0,3) or are the points to be 3 points apart?

I just don't get word problems?!?!?!

 

[plur222]

Re: Exponential Growth (WORD PROBLEM)

So I got some points on the graph starting at the 0 for time and 100 for infection.
(0,100) (0.5,200) (1,400) (1.5,800)
Because the infection doubles every half an hour

How am I to use the method of transformations?

 

[plur222]

I'm lost....... HELP!

Using the method of transformations I got the following equation:

p(t) = 2^t
p(t) = 100 x 2^t
p(2) = 100 x 2^2t

100 being the Distortion on Y
2 being the Base
2t being being the Distortion on X

However ..... when I use this I get the following points to graph

Y (0,1) (1,2) (2,4)
Y1 (0,100) (1,200) (2,400)
Y2 (0,100) (2,200) (4,400)

If I make a chart with t on one side, and p(t) = 100 x 2^2t on the other I get the following points to graph

(0,100) (0.5,200) (1,400) (1.5, 1600) (2,3200) (2.5,6400) (3,12800)

Now the second calculations make more sense because the bacteria supposedly split and double every half hour ... but I don't know how to make the transformation say that?!?!?!

Anyone have any ideas???

 

[Deleted member 4993]

I'm lost....... HELP!

Using the method of transformations I got the following equation:

p(t) = 2^t
p(t) = 100 x 2^t
p(2) = 100 x 2^2t

100 being the Distortion on Y
2 being the Base
2t being being the Distortion on X

However ..... when I use this I get the following points to graph

Y (0,1) (1,2) (2,4)
Y1 (0,100) (1,200) (2,400)
Y2 (0,100) (2,200) (4,400)

If I make a chart with t on one side, and p(t) = 100 x 2^2t on the other I get the following points to graph

(0,100) (0.5,200) (1,400) (1.5, 800) (2,1600) (2.5,3200) (3,6400)

Now the second calculations make more sense because the bacteria supposedly split and double every half hour ... but I don't know how to make the transformation say that?!?!?! ? transformation would not say that - the original exponential function (2[sup:1gysu62s]t[/sup:1gysu62s]) says that - that is the population is doublng after a given amount of time.
Anyone have any ideas???

 

[plur222]

You enjoy being vague don't you...

What starting points do I use for the transformation then?

Do I have the function right?