Find a formula for the exponential function passing through the points $\left(-2, \frac{3}{4}\right)$ and $(1,6)$
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Step 1 ：Given two points (-2, 3/4) and (1,6), we need to find the exponential function that passes through these points. The general form of an exponential function is \(y = ab^x\).

Step 2 ：We can use these points to form two equations. From the point (-2, 3/4), we get the equation \(\frac{3}{4} = ab^{-2}\). From the point (1,6), we get the equation \(6 = ab\).

Step 3 ：Solving this system of equations gives three possible pairs of values for a and b. However, since we are dealing with an exponential function, we discard the solutions involving complex numbers.

Step 4 ：The solution is \(a = 3\) and \(b = 2\). This gives us the exponential function \(y = 3 \cdot 2^x\).

Step 5 ：\(\boxed{y = 3 \cdot 2^x}\) is the exponential function passing through the points (-2, 3/4) and (1,6).