Calculus questions Again

You Already helped me with those questions excepting my confessor made a typo.1.   Suppose we feel a population that increases
according to the controlmula P(t) = P0
ekt.  Our goal
is to satisfy extinguished the controlthcoming table:

Point

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t

P(t)

A

0

B

10

20

C

30

50

D

40

E

2000

(i) 
Use
points B and C to transcribe brace equations. 
Then interpretation them to rerework-out control P0 and k.  Finally, transcribe the
population equation.
(ii) 
Use
(i) to satisfy in the pause of the chart. 
You may finished each treastrong to the neapause tenth.
(iii) 
Now
interpretation your controlmula to mention the doubling occasion of this population.
(iv) 
Explain
how, withextinguished using an equation, you can now apportion the t treasures control which P(t) correspondents
1000. And how abextinguished 250?  Do this by
writing a plain inconsiderable oration, with finished English sentences.
(v) 
Now
on graph tract, inhale a plain graph of this exponential operation. Be strong to
designate your axes, and to designate, with their coordinate, each of objects A through
E.
2.  Consider the controlthcoming
situation:  A foe of with feeling O(0,0), radius 10m, is inscribed in a
square. The ray of bias 30O, in rule aspect, intersects the
foe at object B, and continues to
intersect the clear at object C. Let
A personate (10,0). 
(i) 
Sketch
the symbol involved in the aloft cognomen.
(ii) 
Find
the lawful coordinates of A, B, and C, and designate them on your inhale.
(iii) 
Now
suppose we feel selfish sharp bias Q  (in
radians, instead of the 30O).  Again inhale the inhale!
(iv) 
Again
symbol extinguished the lawful coordinates of A, B,
and C and designate them on your inhale.
NB: You obtain interpretation trig operations here!
(v) 
Now
symbol extinguished the equation you would feel to rerework-out to perceive Q to make
the area of ABCA lawfully correspondent to the
area of the sector.  HINT: This means
area of sector is half area of triangle. (You canreferable rerework-out such an equation
accurately ? this is an specimen of a TRANSCENDENTAL equation, so the theorems of
algebra do referable use.)

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