The fox population in a certain region has an annual growth rate of 9% per year. In the year 2012, there were 20,700 foxes counted in the area. What is the fox population predicted to be in the year 2020? Round to the nearest fox.
#Foxes
To find the fox population in the year 2020, we can use the formula for exponential growth:
P(t) = P0 * (1 + r)^t
Where:
P(t) = population at time t
P0 = initial population
r = growth rate
t = time in years
Given:
P0 = 20,700
r = 9% = 0.09
t = 2020 - 2012 = 8 years
Using this information, we can calculate the fox population in the year 2020:
P(2020) = 20,700 * (1 + 0.09)^8
Calculating further:
P(2020) = 20,700 * (1.09)^8
P(2020) ≈ 20,700 * 1.999710577
P(2020) ≈ 41,399.5579
Rounded to the nearest fox, the fox population predicted to be in the year 2020 is 41,400.
To predict the fox population in the year 2020, we can use the formula for exponential growth:
P(t) = P₀(1 + r)^t
Where:
P(t) = population at time t,
P₀ = initial population,
r = annual growth rate,
t = time in years.
In this case, the initial population (P₀) is given as 20,700 foxes, and the annual growth rate (r) is 9% or 0.09. We want to find the population in the year 2020, which is 8 years after 2012.
Substituting the given values into the formula, we have:
P(2020) = 20,700(1 + 0.09)^8
Calculating the value inside the parentheses first, we get:
1 + 0.09 = 1.09
Then, we raise 1.09 to the power of 8:
(1.09)^8 = 1.99954035
Rounding this value to the nearest fox, we have:
P(2020) ≈ 20,700 * 1.99954035 ≈ 41,396 foxes
Therefore, the fox population predicted to be in the year 2020 is approximately 41,396 foxes.
that is 8 years away, so
20700*1.09^8