Thursday+February+4,+2010Set+6

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Problem 1 Ron Changing the window will not help the friend see the correct graph because he has entered the wrong function. PEMDAS applies. He has incorrectly placed "5x" in the equation without parenthesis. The calculator registered this as 1.12 raised to the 5th, times x. To see the correct function, he had to write it as "1.12^(5x)" This is such a good clear answer!

Problem 2 Charlie

Problem 3 Chris The graphs of //f(x)=a^x// when a>1 and //g(x)=b^x// when 1>b>0 are both similar and different. They are similar because they are both exponential functions and have a y-intercept of 1. They are different because when a>1, the graph is increasing. When 1>b>0, the graph is decreasing. Also, the rate of change for the graphs may vary depending on the value of a or b. The farther the number is from 1, the greater the rate of change. Nice answer!



Problem 4 Avi (-3,5/8) (2,20) Good! a y=mx+b m=(5/8-20)/(-3-2)=31/8 (5/8)-((31/8)*-3)=b=49/4 y=(31/8)x+49/4 b y=a(b)^x 5/8=a*b^-3 a=5/(8b^-3) 20*(8/5)=b^5 32=b^5 b=2 20=a2^2 a=5 y=5*(2)^x

Problem 5a Augustine I get y = 3*5^x

Problem 5b Sam P. y = 48 * (1/2)^x

Problem 5c Rafa y = ab^x 4 = ab^(1/2) divide by "b^(1/2)" 4b^(-1/2)= a (other equation) 2(root 2) = ab^(1/4) 2(root 2) = 4b^(-1/2) times b^(1/4) 2(root 2) = b^(-1/4) [2(root 2)] / 4 = b^ (-1/4) [(root 2) / 2 = b^ (-1/4)]^-4 16/8= b b=2 a=2.378? y=2.378 * 2^x

Problem 6 Sarah The two points on the graph are (2,100) and (0,1) Y= A x B^X 1 = A x 1 therefore A = 1 B^2 x 1 = 100 B = 10
 * 1 = A x B^0**
 * 100 = A x B^2**

Therefore the final equation is
 * y = 10^x**

Problem 7 Nate

Problem 8 unclear; sorry!

__Problem 9 Julia__ two coordinate points: (0,1.2) (2, 4.8) since y = a * b× the two equations will be: 1.2= a * b⁰ 4.8= a * b² a= 1.2 since b⁰ is 1 (anything to the zero-eth is one) since a= 1.2, 4.8= 1.2 * b² in order to isolate b, we divide 4.8 by 1.2--> 4.8 ÷ 1.2= 4 so, since 4= b² which simplified is 2=b

the equation is: y= 1.2 * 2× Good!!

Problem 10 Becca two points= (0, 1.2)(2, 4.8) also good work!

Problem 11Jonathan f(x) - linear, because it has a constant slope. m = .87965 2.19912 = b therefore **f(x) = .87965x+2.19912**

g(x) - exponential because there is not a constant slope. 1.25663 = a 1.38996 = 1.25663 x b^1 1.10610 = b


 * g(x) = 1.25663(1.10610)^x**

h(x) - exponential because there is not a constant slope I did not find that it was exactly exponential either! 2.82743 = a 3.77375 = 2.82743 x b^1 1.33269 = b


 * h(x) = 2.82743(1.33469)^x**

Problem 12 James Does this satisfy the other points in the table?

(0,12) (1,10) C=concentration T=time

12=a(b)^0 a=12 10=12(b)^1 b=(5/6)

C=12(5/6)^T

12=12(5/6)^1 12=12

Problem 13 Jeremy This is the result I found when tested two points.

(1,4096) (2,1024)

A x B^x = y A x B^1 = 4096 1024 = 4096/B x B^2 A = 4096/B 1024B = 4096 x B^3 B/4 = B^3 B = 4B^3 4B^2 = 1. B^2=1/4 B= 1/2 A= 8192

When I tested another 2 points, these were my results:

(2, 1024) (4, 64)

1024 = A x B^2 64 = A x B^4

A = 1024/B^2 64= 1024/B^2 x B^4 64B^2 = 1024 x B^6 64 = 1024B^4 1/256 = B^4 B= 1/4 A= 8192

This can't be a function because the A and B values can't be different.

T