The rigth equation to anticipate the profit after t years is p(t) = 10,000 (1.075)^t
So, given that both store A and store B follow the same equations but t is different for them, you can right:
Store A: pA (t) 10,000 (1.075)^t
Store B: pB(t'): 10,000 (1.075)^t'
=> pA(t) / pB(t') = 1.075^t / 1.075^t'
=> pA(t) / pB(t') = 1.075 ^ (t - t')
And t - t' = 0.5 years
=> pA(t) / pB(t') = 1.075 ^ (0.5) = 1.0368
or pB(t') / pA(t) = 1.075^(-0.5) = 0.964
=> pB(t') ≈ 0.96 * pA(t)
Which means that the profit of the store B is about 96% the profit of store A at any time after both stores have opened.
It’s still 50/50. Flipping coins is purely chance. There isn’t an actual pattern, our brain just create one to make sense of things!
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