[Get Answer ]-Calculus Questions Again

Question Description

You Already helped me with those questions but my professor made a typo.

1.   Suppose we have a population that increasesaccording to the formula P(t) = P0ekt.  Our goalis to fill out the following table:

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Point

t

P(t)

A

0

B

10

20

C

30

50

D

40

E

2000

(i) Usepoints B and C to write two equations. Then use them to solve for P0 and k.  Finally, write thepopulation equation.

(ii) Use(i) to fill in the rest of the chart. You may round each value to the nearest tenth.

(iii) Nowuse your formula to determine the doubling time of this population.

(iv) Explainhow, without using an equation, you can now calculate the t values for which P(t) equals1000. And how about 250?  Do this bywriting a clear brief essay, with complete English sentences.

(v) Nowon graph paper, draw a clear graph of this exponential function. Be sure tolabel your axes, and to label, with their coordinate, each of points A throughE.

2.  Consider the followingsituation:  A circle of with center O(0,0), radius 10m, is inscribed in asquare. The ray of angle 30O, in standard position, intersects thecircle at point B, and continues tointersect the square at point C. LetA denote (10,0). 

(i) Sketchthe figure indicated in the above description.

(ii) Findthe exact coordinates of A, B, and C, and label them on your sketch.

(iii) Nowsuppose we have arbitrary acute angle Q  (inradians, instead of the 30O).  Again draw the sketch!

(iv) Againfigure out the exact coordinates of A, B,and C and label them on your sketch.NB: You will use trig functions here!

(v) Nowfigure out the equation you would have to solve to find Q to makethe area of ABCA exactly equal to thearea of the sector.  HINT: This meansarea of sector is half area of triangle. (You cannot solve such an equationexactly – this is an example of a TRANSCENDENTAL equation, so the theorems ofalgebra do not apply.)

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