A business owner opens one store in town A. The equation mc024-1.jpgrepresents 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

A business owner opens one store in town A. The equation mc024-1.jpgrepresents 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?

Answer 1

Since the profit from the store in town B is predicted to increase at the same rate as the profit from the store in town A, we can represent the profit from the store in town B using the same equation mc024-1.jpg as the profit from the store in town A.

Therefore, at any time after both stores have opened (t>0), the profit from the store in town B will be equal to the profit from the store in town A multiplied by the same rate.

In other words, the profit from the store in town B will always be proportional to the profit from the store in town A.

Answer 2

To compare the profit from the store in town B with the profit from the store in town A at any time after both stores have opened, we need to examine the equation mc024-1.jpg that represents the anticipated profit after t years.

Let's assume the equation is: P(t) = at + b, where P(t) represents the profit after t years, a represents the rate at which the profit increases, and b represents the initial profit.

Given that the initial profit from both stores is the same, we can say that the initial profit for both stores in town A and B is b.

Now, since the profit from the store in town B is predicted to increase at the same rate as the profit from the store in town A, the rate of increase, a, will be the same for both stores.

Therefore, the equation representing the profit from the store in town B would also be: P(t) = at + b.

From this, we can conclude that the profit from the store in town B will always be equal to the profit from the store in town A, as they both follow the same equation and initial profit.