[Victor Sirelson]

Class Discussion on Exponential models.

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

[Sora]

?

[Mona Alzandani]

f(x) = 350e^0.0733t

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

Question:
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.
Q(t)=Pe^rt

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

Q(t)=

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]

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?

A=P(1+R)^t

[Mona Alzandani]

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

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

Solution:
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:

sin(α+β)=
cos(α+β)=
tan(α+β)=

• This reply was modified 5 years ago by Johnny Lai Pan.

[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.

[dlovitt]

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.

[Faisal]

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