MAT1375 D557 Sirelson Spring2019

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  • Class Discussion #1
  • #53459

    Victor Sirelson

    Class Discussion on Exponential models.

    Find an example of an exponential model and post it in this discussion.





    Mona Alzandani

    f(x) = 350e^0.0733t

    A(t) is the number of bacteria
    t represents time in minutes

    How long will it take for the number of bacteria to double?


    Victor Sirelson

    SO, how do we think about this?


    Johnny Lai Pan

    I think this is a great idea to help one another on a open discussion space like openlab.


    Johnny Lai Pan

    Would someone like to help me out on this problem? Having a hard time.
    Studies show that the maximum half-life of Buprenorphine is 3 days.
    Use the following to construct a function that will model the maximum amount of Buprenorphine left in the body after an initial dose of 10 mg.

    Where Q(t) describes the amount of Buprenorphine left in the body after t hours following an initial dose of P mg.


    How long (in hours) will it take for the amount of Buprenorphine left in the body to reach 4 mg?


    Victor Sirelson

    So no one has a suggestion for Johnny?

    If the half-life is 3 days, then after 3 days the initial dose of 10 mg is reduced to half of 10, which is 5.

    Perhaps you can set up the model as 5 = ………..



    Abigail Perez

    The population of Henderson City was 3,381,000 in 1994, and is growing at an annual rate of 1.8%. If this growth rate continues, what will the approximate population of Henderson City be in the year 2000?



    Mona Alzandani

    A(6) = 3381000(1 + 0.018)^6

    R = rate if growth
    P = initial population
    t = difference number of 1994 and 2000

    A(6) = 3381000(1 + 0.018)^6
    = 3381000(1.018)^6
    = 3381000(1.112978226)
    = 3762979.382
    You can try and enter it into webwork the way it is shown above or you could simply convert it to billions like so: 3,762,979,382


    Mona Alzandani

    Part 1:
    Q(t) = 10(.5^(t/72))

    Part 2:
    4 = 10(.5^(t/72))
    (Divide 10 from both sides)
    4/10 = .5^t/72
    (Multiply by (In) to bring the exponent down)
    In(4/10) = t/72 In(.5)
    (Divide In(.5) on both sides)
    In(4/10)/In(.5) = t/72
    (Multiply both sides by 72)
    (In(4/10)/In(.5)) x 72 = t
    95.178 = t


    Johnny Lai Pan

    A little stuck on the this problem.

    Given that α is in quadrant 2 and sin(α)=5/8,
    and also given that β is in quadrant 1 and tan(β)=2/9,
    give an exact answer for the following:



    Victor Sirelson

    I found it helpful to draw a right triangle in the given quadrant, and to label it according to the given values. So sin(α) = 5/8 in Q2 would give a triangle with the x-side to the right (minus) and the y-side up. Then the y-side = 5 and the hypotenuse = 8 and I can calculate the x-side.

    Using this I can get the values for all of the trig functions for α. I do the same for β

    Then I write down the expression for the sin( α+β) = and I can now use the values I have already determined from my two triangles.


    Johnny Lai Pan

    Thank you Prof. I understood what you were explaining during class and here.



    Let’s go back to our problem and list all solutions for sin(x)=1/2
    sin⁡(x)=1/2 in [0,2π)

    x=(pi/6), ((5pi)/6)

    Now, list all solutions for sin(x)=1/2
    sin⁡(x)=1/ in (−2π,0]

    I understand how I got the first one but for some reason I am not understanding the second part.



    basically you do the same thing but instead of adding 2pi, do minus 2pi

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