How do you solve f(x)=a(2^kx) with f(0)=10 and f(3)=640. Find f(2).?

1 Answer
Shiva Prakash M V
Aug 6, 2018

#f(x)=10xx2^(2x)#
#f(2)=160#

Explanation:

#f(x)=axx2^(kx)#
#f(0)=10#
#f(3)=640#
#f(2)=?#
#10=axx2^(kxx0)#
#10=axx1#
#a=10#
#640=axx2^(kxx3)#
#640=10xx2^(3k)#
#640/10=2^(3k)#
#2^(3k)=64#
#2^(3k)=2^6#
#6=3xx2#
#2^(3k)=2^(3xx2)#
Comparing
#k=2#

Thus,
with a=10; k=2
#f(x)=axx2^(kx)# becomes
#f(x)=10xx2^(2x)#
#x=2#

#f(2)=10xx2^(2xx2)10xx2^4=10xx16=160#
#f(2)=160#

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