Answer:
13.5 years
Step-by-step explanation:
The multiplier of the population each year is 5% less than 1, so is 0.95. Then the population in t years is multiplied by 0.95^t. We want to find t such that this value is 1/2.
0.50 = 0.95^t
log(0.50) = t·log(0.95)
log(0.50)/log(0.95) = t ≈ 13.5134 ≈ 13.5
The population will decline to half its original value in approximately 13.5 years.
