Answer:
(i) The increase expected in the share price between the first year and the third year is $0.90
(ii) The 10th year
Step-by-step explanation:
(i) The given relation is [tex]V = 2.95+2\cdot log_{10}\left (10\cdot t + 1 \right )[/tex]
In the first year, we have t = 1, which gives;
[tex]V = 2.95+2\cdot log_{10}\left (10\times 1 + 1 \right ) = 2.95+2\cdot log_{10}\left (1 1 \right ) = \$5.03[/tex]
In the third year, we have t= 3 which gives;
[tex]V = 2.95+2\cdot log_{10}\left (10\times 3 + 1 \right ) = 2.95+2\cdot log_{10}\left (31 \right ) = \$5.93[/tex]
Therefore, the increase expected in the share price between the first year and the third year is $5.93 - $5.03 = $0.90
(ii) When the share price value becomes >$7.00, we have;
[tex]7 = 2.95+2\cdot log_{10}\left (10\cdot t + 1 \right )[/tex]
Which gives;
7 - 2.95 = 2·㏒(10·t + 1)
4.05/2 = ㏒(10·t + 1)
2.025 = ㏒(10·t + 1)
[tex]10^{2.025} = 10 \cdot t + 1[/tex]
105.93 = 10·t + 1
104.93 = 10·t
t = 104.93/10 = 10.493 ≈ 10.5 years which is within the 10th year.
