A population of 1,750 cheetahs decreases by 11% per year. How many cheetahs will there be in the population after 10 years? Round your answer to the nearest whole number.
A. 4,969
B. 486
C. 546
D. 1,640
B?
Total Number of Cheetahs = 1750 x .89^10
(.89 comes from 1 - .11)
1750 x .89^10 = 546
so C
To find the number of cheetahs in the population after 10 years, we need to calculate the population after each year.
The population decreases by 11% each year, which means it remains at 89% (100% - 11%) of its previous value.
After 1 year, the population will be: 1,750 * 0.89 = 1,556.5 (approximately 1,557)
After 2 years, the population will be: 1,557 * 0.89 = 1,385.73 (approximately 1,386)
Proceeding in the same way, after 10 years, the population will be: 1,750 * 0.89^10 ≈ 1,640
Rounding to the nearest whole number, there will be approximately 1,640 cheetahs in the population after 10 years.
Therefore, the correct answer is D. 1,640.
To find the number of cheetahs in the population after 10 years, we need to calculate the decrease in population each year for 10 years and subtract it from the initial population.
First, let's calculate the decrease in population for one year.
11% of 1,750 = 0.11 * 1,750 = 192.5
This means that the population decreases by 192.5 cheetahs each year.
To find the population after 10 years, we multiply the decrease in population per year by the number of years:
192.5 * 10 = 1,925
So, after 10 years, the population decreases by 1,925 cheetahs.
Now, subtract the decrease from the initial population:
1,750 - 1,925 = -175
Since we can't have a negative number of cheetahs, the population will be zero.
Therefore, the correct answer is none of the options provided.