SOLUTION: A bacteria culture starts with 800 bacteria. Two hours later there are 1,280 bacteria. Find an exponential model for the size of the culture as a function of time t in hours. f(t)

Algebra.Com
Question 1179797: A bacteria culture starts with 800 bacteria. Two hours later there are 1,280 bacteria. Find an exponential model for the size of the culture as a function of time t in hours.
f(t) =______

Correct: Your answer is correct.
Use the model to predict how many bacteria there will be after 2 days. (Round your answer to the nearest hundred thousand.)
_____ bacteria
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!
more than one way to do this






and then you can say .
That would be for t in HOURS. You want the appropriate adjustment for DAYS.



--
--

-
For 2 days, t is 48.
Answer by ikleyn(52790)   (Show Source): You can put this solution on YOUR website!
.

An exponential model has the form


    N(t) = , 


where "a" is the initial number of bacteria, "b" is the base of the exponential function and t is the time in hours.


In our case,  the initial value is  a = 800; so we can write this equation


    1280 = ,


describing the scene in 2 hours.


From this equation,


    b =  =  = 1.264911.


So, your exponential function is


    N(t) = .     ANSWER


First question is answered.


To answer the second question, substitute t = 48 hours ("2 days") into the formula


    N(24) =  = 63382376.      ANSWER

--------------

The problem is fully solved.


//////////////


To see many similar  (and different)  solved problems on bacteria growth,  look into the lesson
    - Bacteria growth problems
in this site.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic "Logarithms".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.



RELATED QUESTIONS

A bacteria culture starts with 800 bacteria. Two hours later there are 1,280 bacteria.... (answered by josgarithmetic,ikleyn)
A bacteria culture starts with 1,200 bacteria. Two hours later there are 1,800 bacteria.... (answered by josgarithmetic)
A bacteria culture starts with 1,200 bacteria. Two hours later there are 1,800 bacteria.... (answered by josgarithmetic)
A bacteria culture starts with 1,000 bacteria and doubles in size every 2 hours. Find an... (answered by nerdybill)
A bacteria culture starts with 1,000 bacteria and doubles in size every 3 hours. Find an (answered by ewatrrr)
A bacteria culture starts with 600 bacteria and after 3 hours there are 2400. Find the... (answered by ewatrrr)
The number of bacteria in a culture is increasing according to the law of exponential... (answered by ankor@dixie-net.com)
A bacteria culture starts with 6500 bacteria. After 2.5 hours,there are 208000 bacteria... (answered by Boreal)
A culture of bacteria triples every 8 hours. if there are 100 bacteria now, and 2700... (answered by Solver92311)