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charle [14.2K]
2 years ago
7

Can you please help with this question about exponential equations?

Mathematics
1 answer:
RSB [31]2 years ago
3 0

Since t represents the number of years passed since 2005, in 2005 we have t=0, and in 2015 we have t=10. Let P_J(y),P_D(y) represent the profits of Jones and Davis, respectively, at year y.

We have

P_J(2005) = 10(0.99)^0 = 10,\quad P_J(2015) = 10(0.99)^{10}\approx 9

P_D(2005) = 8(1.01)^0 = 8,\quad P_D(2015) = 8(1.01)^{10}\approx 9

Choosing the best company somehow depends on how much time you can wait: Jones start with a higher value (10 vs 8), but it has a descending trend, because the multiplicative factor 0.99^t goes to zero as t grows.

On the other hand, Davis starts with a smaller value, but 1.01^t tends to infinity as t grows.

So, if you need an immediate result, the most valuable company is Jones, otherwise you're certain can Davis will eventually become bigger.

More precisely, we have

8\cdot 1.01^t = 10\cdot 0.99^t \iff 0.8 = \left(\dfrac{0.99}{1.01}\right)^t \iff t\approx 11

So, after 11 years, Davis will overcome Jones.

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