The fox population in a certain region has an annual growth rate of 10℅ per year. In the year 2012, there were 2100 foxes counted in the area. What is the fox population predicted to be in the year 2018? Round to the nearest fox.
P(x)= 2100 * 1.01^6
= 2100* 1.0615201506
= 2229.1923162= 2229
This the wrong answer what did i do wrong. Please help.
you calculated 1% growth instead of 10%
2100 * 1.1^6
Your 1.01^6 represents an increase of 1%, not 10%
try 1.1^6
1.1^6=1.771561
1.771561*2100=3720.28
To calculate the fox population in the year 2018, we need to use the given annual growth rate of 10% per year.
The formula to calculate compound interest is: A = P(1 + r/n)^(nt), where:
A = the final amount (fox population in this case)
P = the initial amount (fox population in 2012)
r = annual interest rate (growth rate in this case, which is 10% or 0.10)
n = number of times interest is compounded per year (since it's an annual growth rate, n is 1)
t = number of years
Applying this formula to find the fox population in 2018:
P(2012) = 2100
r = 0.10
n = 1
t = 2018 - 2012 = 6 years
Calculating the fox population using the formula:
A = P(1 + r/n)^(nt)
= 2100(1 + 0.10/1)^(1*6)
= 2100(1 + 0.10)^6
= 2100(1.10)^6
= 2100(1.771561)
≈ 3720.28
Therefore, the fox population predicted to be in the year 2018 is approximately 3720 foxes.