How do I calculate this?

Question

Imagine one morning at precisely 6:00 a.m., you find a gold nugget under your pillow. Attached is a note. The note states that, if you leave your nugget under the pillow, each hour-on the hour-it will create twice as many new nuggets as the previous hour. In other words, at 6:00 a.m. one nugget is under your pillow, then at 7:00 a.m. two new nuggets for a total of three, at 8:00 a.m. four new nuggets for a total of 7. Assuming this pattern continues until about 5:30 p.m. that evening, how many golden nuggets would you have collected under your pillow?

Answer 1

S_n = a₁(1 - rⁿ) / (1 - r)         Learn it or know where you can find it!

n = 12 (look at the clock

 

S₁₂ = 1(1 - 2¹²) /(1 - 2)

 

Can you calculate and answer?