Answer :
a. We know the rates of change for both companies, as well as the starting values in 2013. So, to predict the values in 2022 we have to simulate the passing of 9 years. Company A loses 0.22 billions per years, so they will lose [tex] 0.22\cdot 9 = 1.98 [/tex] billions in 9 years. So, we have
[tex] A_{2022} = 4.9 - 1.98 = 2.92 [/tex]
Similarly, company B will have
[tex] B_{2022} = 1.64 + 0.19\cdot 9 = 3.35 [/tex]
billion dollars in 2022.
b. This question is similar to the previous one, except this time we have to find the number of years necessary to reach a particular goal. We have
[tex] 4.9 - 0.22x = 4.24 [/tex]
Solving for x, we have
[tex] x = \dfrac{4.9-4.24}{0.22} = \dfrac{0.66}{0.22} = 3 [/tex]
c. We know the behaviour of the two values, so the number of years will again be the unkown, and we set the two values to be the same:
[tex] 4.9 - 0.22x = 1.64+0.19x [/tex]
Solving for x, we have
[tex] 4.9-1.64 = (0.22+0.19)x \iff 3.26 = 0.41x \iff x = \dfrac{3.26}{0.41} \approx 7.9 [/tex]