A business owner opens one store in town A. The equation p (x) = 10,000 (1.075) represents the anticipated profit after t years. The business owner opens a store in town B six months later and predicts the profit from that store to increase at the same rate. Assume that the initial profit from the store in town B is the same as the initial profit from the store in town A. At any time after both stores have opened, how does the profit from the store in town B compare with the profit from the store in town A?

Question

Bella

Mathematics

31 July, 02:03

A business owner opens one store in town A. The equation p (x) = 10,000 (1.075) represents the anticipated profit after t years. The business owner opens a store in town B six months later and predicts the profit from that store to increase at the same rate. Assume that the initial profit from the store in town B is the same as the initial profit from the store in town A. At any time after both stores have opened, how does the profit from the store in town B compare with the profit from the store in town A?

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Freeman · Answer 1

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.