We know that you use 1 and 1/2 teaspoons to make 8 muffins. We also know that there are 12 muffins in a dozen. If we're trying to make 3 dozen, and there are 12 in a dozen, that means we're trying to make 36 muffins in total.
If 1 1/2 teaspoons of baking powder makes 8, then:
36/8 =4.5.
This means that you need 4.5 times the original amount of baking powder in order to make this patch of 36 muffins (this is because you're increasing the size of the batch by 4.5).
You would simply multiply 4.5 by the amount of baking powder to make 8 muffins, so:
4.5 x 1.5 tsp = 6.75 tsp of baking powder is needed to make 3 dozen muffins.
