Have you iterated your recursive function today?
pg 470 #1,2,3,9, #11-21 Odd
You do NOT need to do ALL of these review problems, but you should do several as practice...
Unit 7 Review (Exclude fractional exponents and section 7-5)
Very limited problems in section 7-8; you will NOT be asked to write a recursive or explicit formula
pg 475-479 #10,12,14,19,25,31,32,33,44,49,50,65,68,71,75,77,80,81
If you want to do extra work in the Chapter Test (pg 479) exclude the following problems:
EXCLUDE #4,6,7,8,9,10,22
On problem 12 of the packet you gave me after school (Section 7-1) Im confused because Im not sure whether I should evaluate the expression first. Its x^0z^0. I get 1x1=1. Im not sure if I should substitute the numbers in first?!?!?!?!!
ReplyDelete-Ethan Chase
If you SIMPLIFY the expression, you get an EQUIVALENT expression, yes?
DeleteIf the original expression is x^0 z^0, well, (as you indicate) we know that anything to the zero power is ONE. So (IN THIS CASE) it just so happens that it doesn't even matter what the values of x and z are (well, as long as they are not = zero, since that would cause an issue).
For simple expressions, it might seem like it doesn't matter whether you
a) simplify first and then substitute/evaluate OR
b) just substitute/evaluate without simplifying
I think you will find as we move into more complex expressions (three cheers for COMING ATTRACTIONS!) it will save you time and effort to simplify first.
Either way, you should get the same answer, yes?
Oh and how do you graph a function like f(x)=2.5^x?
ReplyDelete-Ethan Chase
well, y=f(x)=2.5^x... you can use a calculator for this one and create a table of values for x, such as {-4, -2, 0, 2, 4}... the question could also be phrased as:
DeleteFind the range of the function f(x)=2.5^x using the domain {0,1,2,3}
Recall that the range is the list of y-values and the domain is the list of x-values.
Capeesh?
One last question...
ReplyDeleteHow do you tell if something is Exponential Growth or Decay? I cant get ti without a word problem!
-Ethan Chase
Please RE-READ (see your prior homework assignments) Section 7-7 "Exponential Growth & Decay" pages 460-463 ESPECIALLY the highlighted boxes for exponential GROWTH (pg 460) and DECAY (pg 462). Then let me know if you still have a question.
DeleteMr.C I'm confused on how you would solve #13 on the Chapter Test! Could you explain how to solve it??
ReplyDeleteThe problem states: The human body normally produces about 2 x 10^6 red blood cells per second.
Deletea) use Scientific Notation to express how many red blood cells your body produces in one day.
If I told you that a light bulb flickers twice per second, how many times would it flicker in a day at that rate? Articulate the math you would need to do to solve that problem and then apply the same algorithm to the blood problem.
Part b of the problem states that a pint of blood contains 2.4 x 10^12 red blood cells. You are then asked to calculate how many seconds it would take to replace all of those red blood cells based on the information above. Wouldn't it make sense to divide the red blood cells in a pint BY the number of red blood cells produced every second?
Give parts a&b a try and tell me how you do.
For part 13a. I got 8.64 x 10^4 blood cells in a day. Is that right????
ReplyDeleteWhich is greater? 2 x 10^6 or 8.64 x 10^4? Can the number of cells produced in a second be more than the number of cells produced in a day? Hmmmm, something went wrong somewhere????
ReplyDeleteOops I made a really dumb mistake!!! The 8.64 x 10^4 was the number of seconds in a day. So what I did to fix that is I did (8.64 x 10^4)(2 x 10^6(which are the # of blood cells produced in a second)). My final answer was 1.728 x 10^11. Is that right???
ReplyDeleteAnd then for part b. I got 1.2 x 10^6 seconds. I did 2.4x10^12/ 2x10^6.
The only dumb mistake is one that we are not willing to recognize or correct... neither is the case here.
DeleteYour "new" answers are CORRECT...
... for the second part of part b, can you tell me (in standard notation) what 1.2 x 10^6 seconds is in days??
I'm confused on how you do #25 in the book pages you gave us.
ReplyDeleteRemember, in its most fundamental form, -x can be written as -1*x. Let's use this mathematical tenet to rewrite the original equation.
DeleteORIGINAL:
(x^3 y^5)(-y^7 x)
Since we have ALL MULTIPLICATION, the math gods gift us the associative and commutative properties so that we can re-group, re-order, de-group, or just plain re-arrange to our liking.
RE-WRITE of the ORIGINAL with a leading "-1" and re-ordered and re-grouped we have:
-1*(x^3 * x)(y^5 * y^7)
... too easy now, eh?
-x^4 y^12 it is!!
ALGEBRA ROCKS!! OOM-PAPA-MAUW-MAUW!!
Mr c
ReplyDeleteProblem 33 in the extra problems posted on this blog has to do with a fractional exponent. The question is (x2/3)[]=x^2 do we need to know this?
Danie
No fractional exponents on the test... if I inadvertently assigned one, it was my mistake (apparently there's a first for everything!)...
Deletehi ethan exponential growth is showed as y=a times b^x where b is greater than 1 exponential decay is the same except b is less than one. A is the initial amount, and b is the rate of change. When b is greater than 1, you are multiplying by at least 100 percent, so the initial number, a, is growing. If b is less than 1, you are multiplying by less than 100 percent, so the initial number gets smaller. Soooooo if you had y=4(3)^3 it would grow because you are multiplying by something greater than 1 or 100 percent. If it was y=4(1/3)^3, it would decay, or get smaller, because you are multiplying by less than 1 or less than 100 percent. BASICALLY...."a" times "a number less than 1" equals decay. "a" times "a number greater than 1" equals growth!
ReplyDeleteYup, what he said, yo!
DeleteA thought to ponder... what if the 'b' in y=a*b^x was equal to ONE... instead of less than 1 (decay) or greater than 1 (growth)??
I just wanted to say thanks for explaing problem 13 to me, oh and the number in standard notation is about 14 days or 2 weeks to replace that one pint of blood!
ReplyDelete1) A pleasure AND
Delete2) Yup!