SOLUTION: Find the values of a and b so that the curve y= a * b^x passes through the points (1,6) and (-1, 3/2), given that b>0 I can't seem to find relevant information on this type of p

Algebra ->  Graphs -> SOLUTION: Find the values of a and b so that the curve y= a * b^x passes through the points (1,6) and (-1, 3/2), given that b>0 I can't seem to find relevant information on this type of p      Log On


   

Question 987414: Find the values of a and b so that the curve y= a * b^x passes through the points (1,6) and (-1, 3/2), given that b>0
I can't seem to find relevant information on this type of problem, so i'm not even really sure how to start.
Found 3 solutions by josgarithmetic, solver91311, macston:
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
Take logarithms of both sides of the equation and this gives a linear equation. Also take the logarithms of the y-coordinates of your given points and then use these as points for your linearized form of the equation. You can then use your earlier learned concepts and skills about linear equations and lines.

After done correctly, if using base-ten logarithms, the equation should be equivalent to log%2810%2Cy%29=%28log%2810%2Cb%29%29x%2Blog%2810%2Ca%29, and your converted given points are (1, log(6)) and (-1, log(1.5)).

Use these two points and the formula for slope based on two known points.
log%2810%2Cb%29=%28log%2810%2C6%29-log%2810%2C%283%2F2%29%29%29%2F%281-%28-1%29%29
Keep working with that to simplify as much as possible, and you should find log%2810%2Cb%29=log%2810%2C2%29
meaning obviously,
highlight%28b=2%29
;
You still want to determine the value for "a". You can do this...

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


You might have a better time understanding this if you consider that points on the graph of some function of are of the form . So if is the -coordinate of a point on the graph, then is the -coordinate of that point.

From this idea we get that if is a point on a graph of , Then it must be true that . And if is on the graph, then

So, since , we can write:



Solve for remembering the restriction that . Then substitute into either equation and solve for

John

My calculator said it, I believe it, that settles it

Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
.
y=a%2Abx Use values (-1,3/2)
3%2F2=ab%5E-1
3%2F2=a%2Fb
3b%2F2=a Use this for to substitute for a and (1,6)
.
y=a%2Ab%5Ex
6=3b%2F2%2Ab%5E1
6=3b%5E2%2F2
12=3b%5E2
4=b%5E2
2=b
.
a=3b%2F2 Put in value for b.
a=%283%2A2%29%2F2
a=6%2F2
a=3 Use a=3 and b=2 in original equation
.
ANSWER: y=3*2^x
.
+graph%28+800%2C+800%2C+-10%2C+10%2C+-10%2C+10%2C+3%2A2%5Ex%29+