Question

The amount of money in an investment account (in millions) is given by P(t)=-cos(4t)+39-2t where t is in months. If the amount of money ever exceeds $38 million the manager of the account receives a bonus. During the first 3 months the account is open, does the manager ever receive a bonus?

Answer 1

substitute t = 1, t=2 and t =3 in the equation and see if its value exceeds 38

Answer 2

I understand that I'm finding this on the closed interval [1,3]. I'm having problems with finding the angle other than 4t=.5236 + 2pi(n)

Answer 3

Is it 4t=2.6179 + 2pi(n)?

Answer 4

just because you are finding the cosine of something doesn't mean that that something is an angle. it can be time (in this case) or frequency or anything else. don't worry about converting it to an angle.

Answer 5

Okay I don't know quite how to explain it, but I know I have to find the other equation for the other quadrant.

Answer 6

why? your system is defined by the equation you are given. what is all this talk about quadrants?

Answer 7

Sorry dude. I don't know enough about what I'm talking about to explain. I could show you all the work I've done but I still don't know if I could convey to you what I'm talkin bout.

Answer 8

I'm using examples from my professor's notes to work this problem - I just know that at this point he always finds which quadrants the argument exists in and then evaluates.

Answer 9

Check your notes and see if in all those cases the cosine happened to be in the denominator or numerator of a fraction.

Answer 10

No sir

Answer 11

cosine of both positive and negative numbers always exists.

Answer 12

Right so in which quadrants is inverse sin positive?

Answer 13

2nd quadrant i believe

Answer 14

or rather, in the 1st and 4th quadrants

Answer 15

p(1) = -cos(4)+39-2 = 37.653
p(2) = -cos(8)+39-4 = 35.145
p(3) = -cos(12)+39-6 = 32.156.

Since the principal amount does not exceed 38, the manager does not get a bonus. is that clear?

Answer 16

I have calculated the cosines in radians, I am not sure if you have to convert them to degrees.

Answer 17

That is what I got, also. Yes - I calculate only in radians. Thank you for your time/help!

Answer 18

There are other values besides t = 1, 2, 3... there are also values between them. As it turns out: t = .27728605 produces 38.00000001

Answer 19

you are welcome. It shouldn't make a difference if you are calculating in radians or degrees since cosines cannot exceed 1 on either side.

Answer 20

ah yes, branlegr is right! The problem stated if the manager EVER receives a bonus. you should heed branlegr's advice.

Answer 21

But how do you know to solve for t=.2773?

Answer 22

the problem is ambiguous. Does the statement t is in months mean that t can only take integer values?

Answer 23

Holy crap I'm so confused.
Obviously not, because I solved for P(1.7010), P(2.2253)...etc