## Tutoring Algebra 2 Regents Review

SECTION 2:

## Logarithms Exponentials Absolute Value Problems

__EXAMPLE 1:__

All the answer choices have ln (natural log) in them. This means we will use natural log to solve this problem.

The givens in the problem : a – is a number >0 , b- is a number>0, c- is any number>0, t- is a variable.

E- base of the logarithm in this case natural logarithm, it is a specific number 2.718

Take the log of both sides

Choice (3)

__EXAMPLE 2:__

The question is asking for which value of x, out of the choices given.

OPTION 1) Substituting into the choices.

OPTION 2) Graph both functions to see where they are equal on the graph.

Using the change of base formula it is easy to rewrite the into logx/log3.

To enter absolute value into the calculator hit MATH-> NUM ->abs(

To calculate hit 2^{nd} Calc choose Intersect.

First curve? Hit the first curve, move the mouse x symbol closer to the intersection. Hit enter.

Second curve? Move the mouse of the x on the second curve closer to the intersection. Hit enter.

Guess? Hit enter.

Since there are TWO intersections the same procedure can be applied to finding the second intersection.

Choice (1).

__EXAMPLE 3:__

What is the question asking? The average decreasing rate of change per year.

What is the *average decreasing rate of change*? It is the slope from T – 2012 to T- 2014.

Formula of the slope = Y1- Y2/ X1-X2 (The difference in Y values over the difference in X values)

What are the Y values in this case?

Greg purchased the can in June 2011 which means by June 2012.

The value of the car after ONE year would be t =1.

**The value of the car after one year is 13600.**

The value of the car after THREE years would be t =3.

Y1 = 13600

Y2 = 8704

X1 =1 years

X2= 3 years

(Y1- Y2) /(X1- X2) = average rate of change (decrease from 3 years to 1 year).

Choice (3).

__EXAMPLE 4:__

This question has a lot of information, and the important thing is what is the question asking? The number of grams A of Iridium 192 present after t days is

Given in the question. But then the question asks what is the number of Iridim -192 present after t days?

So the question is asking already what is given in the question itself. This could only mean that there is a different way of expressing A- the number of grams of Iridium present after t days.

Choice (3)

__EXAMPLE 5:__

What are rational Exponents?

- Rational – means involving a ratio ( fraction) one number divided by another 2) fraction can be expressed as a decimal.

- What are the properties of rational exponents?

3 is the denominator of the rational exponent and it becomes the index in the radical.

4 is the numerator of the rational exponent and it becomes the power the radical is taken to.

Simplifying the radical and (-2) ^4 = 16.

Exponents can be integers, positive, negative and zero as well as fractions.

Ref:

More Examples of fractional exponents:

http://www.mesacc.edu/~scotz47781/mat120/notes/exponents/rational/rational_exponents.html

## Comments