You should first recognize the shape of the curve - it's an exponential function, so its equation takes the form [tex]y(x)=a\cdot b^{cx}[/tex] for some constants a, b, and c.
The curve lies above the x-axis, so a must be positive.
The curve is defined everywhere (there are no discontinuities), so b must be positive.
As you move left to right, the function is increasing, so c must also be positive. But to make things simpler, let's assume c = 1.
When x = 0, the curve passes through the point (0, 1). In our equation, we have
[tex]y(0) = a\cdot b^0 = a[/tex]
so it follows that a = 1.
When x = 1, the curve approximately passes through the point (1, 4); so
[tex]y(1) = b^1 = 4[/tex]
so b = 4.
Then the equation of the curve might be [tex]\boxed{y = 4^x}[/tex].
