Difference between revisions of "1998 AJHSME Problems/Problem 16"
Talkinaway (talk | contribs) |
Hashtagmath (talk | contribs) (→Problem 16) |
||
| (6 intermediate revisions by 5 users not shown) | |||
| Line 1: | Line 1: | ||
| − | ==Don't Crowd the Isles== | + | ==Don't Crowd the Isles== |
Problems 15, 16, and 17 all refer to the following: | Problems 15, 16, and 17 all refer to the following: | ||
| Line 8: | Line 8: | ||
| − | + | ==Problem 16== | |
Estimate the year in which the population of Nisos will be approximately 6,000. | Estimate the year in which the population of Nisos will be approximately 6,000. | ||
| Line 14: | Line 14: | ||
<math>\text{(A)}\ 2050 \qquad \text{(B)}\ 2075 \qquad \text{(C)}\ 2100 \qquad \text{(D)}\ 2125 \qquad \text{(E)}\ 2150</math> | <math>\text{(A)}\ 2050 \qquad \text{(B)}\ 2075 \qquad \text{(C)}\ 2100 \qquad \text{(D)}\ 2125 \qquad \text{(E)}\ 2150</math> | ||
| − | ==Solution 1== | + | ==Solution== |
| + | ===Solution 1=== | ||
We could triple the population every <math>25</math> years and make a chart: | We could triple the population every <math>25</math> years and make a chart: | ||
| Line 25: | Line 26: | ||
Year: 2050 | Year: 2050 | ||
| − | Population:1800 | + | Population: 1800 |
Year: 2075 | Year: 2075 | ||
| Line 33: | Line 34: | ||
Population: 16200 | Population: 16200 | ||
| − | The closest is | + | The closest year is 2075, or <math>\boxed{B}</math> |
| − | ==Solution 2== | + | ===Solution 2=== |
We could find out how many periods of 25 years we need to triple by dividing our total from our present number. | We could find out how many periods of 25 years we need to triple by dividing our total from our present number. | ||
| Line 53: | Line 54: | ||
* [[AJHSME Problems and Solutions]] | * [[AJHSME Problems and Solutions]] | ||
* [[Mathematics competition resources]] | * [[Mathematics competition resources]] | ||
| + | {{MAA Notice}} | ||
Latest revision as of 16:52, 17 April 2021
Don't Crowd the Isles
Problems 15, 16, and 17 all refer to the following:
In the very center of the Irenic Sea lie the beautiful Nisos Isles. In 1998 the number of people on these islands is only 200, but the population triples every 25 years. Queen Irene has decreed that there must be at least 1.5 square miles for every person living in the Isles. The total area of the Nisos Isles is 24,900 square miles.
Problem 16
Estimate the year in which the population of Nisos will be approximately 6,000.
Solution
Solution 1
We could triple the population every 
years and make a chart:
Year: 2000 Population: 200
Year: 2025 Population: 600
Year: 2050 Population: 1800
Year: 2075 Population: 5400
Year: 2100 Population: 16200
The closest year is 2075, or 
Solution 2
We could find out how many periods of 25 years we need to triple by dividing our total from our present number.
The power of 
that 
is closest to is 
Therefore, after periods, we will be closest to 
.
See also
| 1998 AJHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 15 |
Followed by Problem 17 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
