Part V. Applying What We Learned. (3) In an optimal environment, a bacteria popu
ID: 3093658 • Letter: P
Question
Part V.Applying What We Learned.
(3) In an optimal environment, a bacteria population growsexponentially. At noon
in the sewage treatment plant, experimenters introduce speciallycultured bacteria
into a barrel full of rich nutrients. We will assume that thebacteria population in
the barrel is modeled by an exponential function.
Let N(t) be the number of bacteria after t days. Then N(t) = Patfor some
constants P and a. Measurements indicate that N(2) = 5, 400 andN(6) = 345, 000.
(a) Before working the problem, estimate (guess!) the value ofN(4), the number
of bacteria at noon on the fourth day.
(b) Write down two equations for P and a, one when t = 2 and theother when
t = 6.
(c) Use these two equations to compute a and P. Round your valuesto three
significant digits, but be sure to store the more precise valuesfor further calculations.
(d) Write down the formula for N(t) using the rounded values of aand P. (But
remember to use the more precise stored values when you use theformula!)
(e) Evaluate N(4), N(7), and N(9). (Give answers to the nearestbacterium.)
(f) Does your guess in (a) agree with your answer in (e)?
(g) Is the precision of your answers in part (e) in agreement withthe measurements
for N(2) and N(6)?
(h) To what extent should the values in (e) be rounded? Explainyour answer
Explanation / Answer
Write down two equations for P and a, one when t = 2 and the otherwhen t = 6. Question b: Okay so I am not sure about this but i believe the equations couldbe : P*a*6=345000 P*a*2 =5400 However this does not seem to work, I really want to try and workthis out with you lets share idea.