The fly population on an island is declining at a rate of 1.7% per year. The population was 4600 in the year 2016.
Which answer is the best prediction of the population in the year 2023?
4010 <my choice
4080
4120
4150
I disagree:
4600*0.983^7 = 4080
To predict the population in the year 2023, we can use the exponential decay formula:
P(t) = P0 * (1 - r)^t
where:
P(t) is the population at time t
P0 is the initial population
r is the decay rate
t is the number of years
Given that the population in 2016 was 4600 and the decay rate is 1.7%, we can calculate the population in 2023 using the formula.
P(2023) = 4600 * (1 - 0.017)^7
P(2023) ≈ 4600 * (0.983)^7
P(2023) ≈ 4600 * 0.8723
P(2023) ≈ 4003.58
So, the best prediction of the population in the year 2023 is approximately 4003, which is closest to the answer option 4010. Therefore, 4010 is the best prediction among the given choices.
To predict the population in the year 2023, we need to calculate the population after 7 years (from 2016 to 2023) based on the decline rate of 1.7% per year.
First, we calculate the population after 1 year:
Population after 1 year = 4600 - (1.7% * 4600)
= 4600 - (0.017 * 4600)
= 4600 - 78.2
= 4521.8
Next, we calculate the population after 2 years:
Population after 2 years = 4521.8 - (1.7% * 4521.8)
= 4521.8 - (0.017 * 4521.8)
= 4521.8 - 76.9
= 4444.9
Continuing in the same manner, we can calculate the population after 3 years, 4 years, 5 years, 6 years, and finally after 7 years.
After performing the calculations, we find that the population in the year 2023 will be approximately 4080.
Therefore, the best prediction for the population in the year 2023 is 4080.