Find the exponential function f(x)=a⋅2^bx with (0,3) and (1,4). a=?,b=?

Answer 1

plug in your values, assuming you meant
f(x) =a (2)^(bx) and not what you typed.

for (0,3) , 3 = a(2)^0 --> 3 = a

for (1,4) , 4 = 3(2)^b
2^b = 4/3
take logs of both sides, and use log rules
b log2 = log4 - log3
b = (log4 - log3)/log2 = appr .415037

Answer 2

thank you!