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The function f(x) = ax^r satisfies f(2) = 1 and f(32) = 4. Find r.

 

 

Thanks dudes!

 #1
avatar+578 
+1

im just going to accept that i am dumb

 Dec 1, 2017
edited by OfficialBubbleTanks  Dec 1, 2017
 #2
avatar+1442 
+1

What if the solution was a fraction?

 #3
avatar+578 
0

do you want hundreds of decimal places?

 #4
avatar+7352 
+2

f(x)  =  ax^r

 

f(2)  =  1

a(2)^r  =  1                  Divide both sides by  2^r .

a  =  1 / ( 2^r)

 

f(32)  =  4

a(32)^r  =  4              Divide both sides by  32^r .

a  =  4 / ( 32^r)

 

Set these two values of  a  equal to each other.

 

1 / ( 2^r)  =  4 / (32^r)         Cross multiply.

32^r  =  4 * 2^r                   And we can write  32  and  4  as powers of  2 .

(2^5)^r  =  2^2 * 2^r

2^(5r)  =  2^(2 + r)

5r  =  2 + r

4r  =  2

r  =  1/2

 Dec 1, 2017
 #5
avatar+1442 
+2

Thanks!


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