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

1 Answer

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