Since [tex] t [/tex] represents the number of years passed since 2005, in 2005 we have [tex] t=0 [/tex], and in 2015 we have [tex] t=10 [/tex]. Let [tex]P_J(y),P_D(y)[/tex] represent the profits of Jones and Davis, respectively, at year y.
We have
[tex]P_J(2005) = 10(0.99)^0 = 10,\quad P_J(2015) = 10(0.99)^{10}\approx 9[/tex]
[tex]P_D(2005) = 8(1.01)^0 = 8,\quad P_D(2015) = 8(1.01)^{10}\approx 9[/tex]
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 [tex] 0.99^t [/tex] goes to zero as t grows.
On the other hand, Davis starts with a smaller value, but [tex] 1.01^t [/tex] 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
[tex] 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 [/tex]
So, after 11 years, Davis will overcome Jones.
