Answer:
8.31 weeks
Step-by-step explanation:
Given that the cost of one share of Apple stock, C=$120
Rate is the increment of the stock value, R= 5%/week=0.05 / week.
Assuming that after t week, the stock has been sold for $180.
Since the stock value increased at 5% every week, so, the interest is compounded weekly, so
[tex]S=C\left(1+R\right)^t \\\\ \Rightarrow 180 = 120\left(1+0.05\right)^t \\\\ \Rightarrow 180 = 120\left(1.05 )^t \\\\[/tex]
[tex]\Rightarrow \frac{180}{120}=1.05^t \\\\\Rightarrow 1.5=1.05^t[/tex]
[tex]\Rightarrow \ln(1.5)=t \ln(1.05)[/tex] [taking log both sides]
[tex]\Rightarrow t=\frac {\ln(1.5)}{\ln(1.05)}=8.31[/tex] weeks
Hence, after 8.31 weeks the stock has been sold for $180.
