#$&*
Mth163
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** Question Form_labelMessages **
q007 describing graphs
** **
From basic algebra recall that a^(-b) = 1 / (a^b).
So, for example:
2^-2 = 1 / (2^2) = 1/4, so 5 * 2^-2 = 5 * 1/4 = 5/4.
5* 2^-3 = 5 * (1 / 2^3) = 5 * 1/8 = 5/8. Etc.
The decimal equivalents of the values for x = 0 to x = 3 will be 5, 2.5, 1.25, .625. These values decrease, but by less and less each time.
The graph is therefore decreasing at a decreasing rate. **
** **
I do not remember this rule from basic algebra a^(-b)= 1/(a^b). I thought that I should use the exponent as a negative and solve. If I use th rule I can solve, but I want to know more so that I can brush up on this. Can you point me in the right direction in the text book???
@&
This is an algebra concept and the textbook is not likely to address it sufficiently.
I recommend that you search the Web using things like
laws of exponents
reasons for laws of exponents
laws of exponents explained
A quick response from me about negative exponents:
2^3 = 8 and 2^4 = 16.
So 2^3 * 2^4 = 8 * 16 = 128.
Also 2^3 * 2^4 = (2 * 2 * 2) * (2 * 2 * 2 * 2), which is clearly 2^7.
This illustrates why, when multiplying powers of the same base, we add the exponents.
Now consider the following:
2^3 * (1 / 2^3) = 2^3 / 2^3 = 1.
2^3 * 2^(-3) = 2^(3 + (-3) ) = 2^0 = 1.
So
2^3 * (1 / 2^3) = 1
and
2^3 * 2^(-3) = 1.
So 1 / 2^3 must be the same as 2^(-3).
*@