Answer: 69 years
Explanation:
y=ab^x
Let y be the number of homicides per year, and x be the number of years since year 0 (the most recent year).
y=1000(0.99)^x
The rate decrease is 1% = 0.01.
We want to know when y = 500.
500 = 1000 * (0.99)^x
0.5 = (0.99)^x
ln(0.5) = ln(0.99^x)
ln(0.5) = x ln(0.99)
x = ln(0.5)/ln(0.99)
x = 68.967563
Round off and you get 69 years.