Answer:
The answer is "6.093 years".
Step-by-step explanation:
The rate of decline in sales in [tex]22\%[/tex] per year.
The starting sales is 100 units:
Using compounding formula:
[tex]\to 100 \times (1-\frac{22}{100})^t=22\% \ of \ 100\\\\\to 100 \times (\frac{100-22}{100})^t=\frac{22}{100} \times \ 100\\\\\to (\frac{78}{100})^t=\frac{22}{100}\\\\\to 0.78^t=0.22\\\\\text{taking \log on both the sides}\\\\[/tex]
taking log on both sides
[tex]\to \log_e \ 0.78^t= \log_e\ 0.22\\\\\to t \log_e \ 0.78= \log_e\ 0.22\\\\\to t = \frac{\log_e 0.22}{\log_e 0.78}\\\\[/tex]
[tex]= \frac{-0.6575}{-0.1079}\\\\= \frac{0.6575}{0.1079}\\\\=6.093[/tex]
