Answer:
Step-by-step explanation:
Heres the complete question:
A uranium mining town reported population declines of 3.2%, 5.2%, and 4.7% for the three successive five-year periods 1985–89, 1990–94, and 1995–99. If the population at the end of 1999 was 9,320:
How many people lived in the town at the beginning of 1985? (Round your answer to the nearest whole number.)
solution:
Let the population of the town at the beginning of 1985 be P. Then, given that in the first five-year period the population declined by 3.2%, i.e., 0.032, the population of the town at the end of 1989 would be
(1 – 0.032)P = 0.968P.
Again, given that in the second five-year period the population declined by 5.2%, i.e., 0.052, the population of the town at the end of 1994 would be
(1 – 0.052)(0.968P) = 0.948 x 0.968P
= 0.917664P.
Finally, given that in the third five-year period the population declined by 4.7%, i.e., 0.047, the population of the town at the end of 1999 would be
(1 – 0.047)(0.917664P) = 0.874533792P.
We are given, 0.874533792P = 9320 or
P = 9320/0.874533792
= 10657.11.
Thus, 10657 people lived in the town at the beginning of 1985
.