Math questions: logarithms?

2015-09-13T12:10:37Z

1. The population of a city is decreasing at the rate of 0.3% annually. How long does it take to reduce 2% of its population?

2. The stock depreciates x%, and then appreciates 20%. Will you get back your money exactly (i.e., $1 if
you invest $1)? What is the value of x?

I have no idea how to set these problems up. I know we have to use logarithms to solve them. Can someone help me out? Thank you!

JB2015-09-13T12:17:17Z

1. (.997)^n = .98, so taking logarithms n log(.997) = log(.98) so n = log(.98) / log(.997) = 6.72 years, or about 6 years and 9 months.