The initial number of transactions that took place in the first hour of day is 10 and the number of transactions doubles every hour after that

I think the question for this problem is to formulate an equation that could describe the behavior of the trend. To do this, let's see the trend first. In the first hour, the number of transactions is 10. In the 2nd hour, the transactions is 2(10) = 20. In the third hour, the transactions is 20(2) = 40. So, we can see that the trend is 10, 20, 40, 80, and so on. You notice that this is a geometric progression, where r=2. Thus, the equation for this will be:

Number of transactions = 10(r)ⁿ⁻¹ = 10(2ⁿ⁻¹), where n is the number of hours

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