The profit from the store in town B compared with the profit from the store in town A is the ratio represented by 96%.
What is a ratio?
The ratio is the simplest form of a fraction involving two quantities determining each other. It is written as a:b, read as "a is to b", and functions as a/b.
How to solve the question?
In the question, we are given that a business owner opens one store in town A. The equation p(x)= 10,000(1.075)^t 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.
We are asked to assume that the initial profit from the store in town B is the same as the initial profit from the store in town A and find the comparison between the profits from the store in town B to the store in town A.
We take the time for the store in town A as t1.
Then the time for the store in town B is t1 - 0.5, as store in town B is opened 6 months after the store in town A.
To compare the profits, we take the ratio of the profits from the stores.
= Profit from the store in town B/Profit from the store in town BA
= 10,000(1.075)^(t1 - 0.5)/10,000(1.075)^t1
= (1.075)^(t1 - 0.5 - t1)
= 1.075^(-0.5)
= 1/(1.075)^0.5
= 0.96448
= 96% (approx.)
Therefore, the profit from the store in town B compared with the profit from the store in town A is the ratio represented by 96%.
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