If Jeff’s worst nightmare plays out, the stock will lose 20% of its value in 12 months. That means that after 12 months, the stock will be worth 1 – 0.2 = 0.8 of its original value. Its value will get multiplied by 0.8 for every 12 months that pass.
Every 12 months the value will be decreased to 0.8 of its earlier value — that is, multiplied by 0.8 of its value — so that after n periods of 12 months each, the value, A, will be the original value, , multiplied by : . In exponential decay, the number that gets taken to a power — 0.8 in this case — is called the decay factor.
But the question asks for the value t months, not n periods of 12 months, after the investment is made. Since n is a period of 12 months and t represents 1 month, Then .