You are on point bhai. Since the curve is exponential, 2^1.5 < 3.
Now you could find the approximate value of \(2^{(1\frac{2}{3})}\) just to make sure that you're marking the correct option. I've already mentioned one way to approximate \(2^{(1\frac{2}{3})}\)in my solution.
Another way is-
\(3375 < 4000 < 4096\)
\(15^3<4000<16^3\)
\(1.5^3 < 4 < 1.6^3\)
\(1.5 < 4^{(\frac{1}{3})} < 1.6\)
\(1.5 < 2^{(\frac{2}{3})} < 1.6\)
\(1.5*2 < 2*2^{(\frac{2}{3})} < 1.6*2\)
\(3 < 2^1*2^{(\frac{2}{3})} < 3.2\)
\(3 < 2^{(1+\frac{2}{3})} < 3.2\)
AnirudhaS wrote:
I solved this by "feeling". Let me explain. But I need experts to critic me on this method.
nick1816 let me know your thoughts please?
So we know
2^1.1
2^1.2
2^1.3
.....
2^1.9
2^2
is going to be an exponential curve (NOT linear).
And if it was linear then 2^1.5 would be exactly 3, but its not.
So 2^1.5 < 3
But the rate of growth of this exponential curve is only slight (not as much as say 2^2, 2^3, 2^4...)
So 2^1.5 should be quite close to 3
I mean then I chose the option B which is closest. However, I do understand that this is not full proof (as we do not know how close 2^1.5 is to 3 unless we work it out)