If b is directly proportional to a2 and b=96 when a=4, find an equation connecting a and b.

Step 1: Understand the problem The problem states that b is directly proportional to a^2. This means that as a increases or decreases, b will increase or decrease by the square of that amount. We also know that when a=4, b=96.

Step 2: Write the proportionality equation In mathematics, direct proportionality is often expressed as b = ka^2, where k is the constant of proportionality.

Step 3: Substitute the given values into the equation We know that when a=4, b=96. So we can substitute these values into the equation to find the value of k. 96 = k*(4^2)

Step 4: Solve for k Solving the equation gives us k = 96 / (4^2) = 6

Step 5: Write the final equation Now that we know k = 6, we can substitute this back into the original equation to get the final equation connecting a and b: b = 6a^2