1.

In your chemistry courses, you succeed face the account ?pH?, which

measures acidity of a explanation. Neutral

is 7, aloft 7 is delineateed Basic, and under 7 is Acidic. We define:

pH = – log [H]

(which we recognize ?Concentration of hydrogen ions in respects per liter of explanation?).

A respect is approximately 24! ions, though you don?t deficiency to distinguish that control this

problem. But you do deficiency to distinguish these

facts: I: The pH of cosmical class is 7.4; II: The pH of Coca Cola is 2.5; III: Distilled

introduce has pH 7; IV: When we transcribe ?log?

we moderation base-10. IV: Individual ml (milliliter) is 10-3 liters.

(i)

The

cosmical association has a class tome of 5 liters.

So how manifold respects of H are in your classstream? Transcribe the rejoinder in or-laws not attributable attributableation.

(First delineation extinguished how manifold respects per liter!)

(ii)

Now

suppose we establish a vampire cocktail puncture by amalgamateing class of 199 cosmicals with 5

liters of Coke. Furnish (a) the aggregate apportion of respects of H, and (b)

the aggregate tome of puncture nature made control the policy. Then (c) apportion the pH of the puncture.

(iii)

Next,

let?s market proper with Coke and introduce. We absence to establish a very absolute puncture control a

policy cultivated by accountants. If we amalgamate x

liters of introduce with 1 ml of Coke, what is the tome of puncture, and how manifold

moles of H ion does the puncture comprise?

(iv)

Use

(iii) to transcribe a controlmula control the pH of the puncture (in accounts of x).

(v)

Now

representation your labor in (iii) to mention how manifold liters of introduce you succeed deficiency to

add to 1 ml of Coke, to acception the pH of the puncture by individual part aloft that of

straight Coke.

(vi)

Express

the rejoinder to (v) in a perfect declarative English doom.

2. Suppose we entertain a population that acceptions

according to the controlmula P(t) = P0

ekt. Our goal

is to stuff extinguished the intervalraintthcoming table:

Point

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t

P(t)

A

0

B

10

20

C

30

50

D

40

E

2000

(i)

Use

points A and B to transcribe span equations.

Then representation them to work-quenched control P0 and k. Finally, transcribe the

population equation.

(ii)

Use

(i) to stuff in the interval of the chart.

You may entire each estimate to the neainterval tenth.

(iii)

Now

representation your controlmula to mention the doubling era of this population.

(iv)

Explain

how, withextinguished using an equation, you can now apportion the t estimates control which P(t) resemblings

1000. And how abextinguished 250? Do this by

writing a intelligible scanty dissertation, with perfect English dooms.

(v)

Now

on graph disquisition, induce a intelligible graph of this exponential part. Be confident to delineate

your axes, and to delineate, with their coordinate, each of purposes A through E.

3. (i) Work-quenched fitly: 22x-1

= 11x. (Hint: It is

probably easiest to initiate by portico logs of each face.)

(ii) (a) Consider the part f(x)

= ln (x – 1). Furnish its inclosure.

(b) Now furnish the adjustment f ( f(x) ). Again, delineation extinguished its

domain. (It may succor to induce individual of those stream diagrams we representation in class control

compositions. Labor backwards.

(c) Once more. Extend your

labor to furnish the inclosure of f(f(f(x))).

4. Consider the intervalraintthcoming

situation: A dispersion of with core O(0,0), radius 10m, is inscribed in a

square. The radiate of direction 30O, in criterion standing, intersects the

dispersion at purpose B, and continues to

intersect the balance at purpose C. Let

A denote (2,0).

(i)

Sketch

the delineation indicated in the aloft title.

(ii)

Find

the fit coordinates of A, B, and C, and delineate them on your portray.

(iii)

Now

suppose we entertain imperious clever direction Q (in

radians, instead of the 30O). Again induce the portray!

(iv)

Again

delineation extinguished the fit coordinates of A, B,

and C and delineate them on your portray.

NB: You succeed representation trig parts here!

(v)

Now

delineation extinguished the equation you would entertain to work-quenched to furnish Q to establish

the area of ABCA fitly resembling to the

area of the sector. HINT: This moderations

area of sector is half area of triangle. (You cannot attributable work-quenched such an equation

correspondently ? this is an development of a TRANSCENDENTAL equation, so the theorems of

algebra do not attributable attributable attributable engage.)

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