Answer:
P(t) = A * (1 + r)^t ;
14,922 ;
Year 2013
Step-by-step explanation:
Given the following :
Continuous growth rate(r) = 5% = 0.05
Population in year 2000 = Initial population (A) = 10,100
Time(t) = period (years since year 2000)
A)
Find a function that models the population,P(t) , after (t) years since year 2000 (i.e. t= 0 for the year 2000).
P(t) = A * (1 + r)^t
Trying out our function for t = year 2000, t =0
P(0) = 10,100 * (1 + 0.05)^0
P(0) = 10,100 * 1.05^0 = 10,100
B.)
Use your function from part (a) to estimate the fox population in the year 2008.
Year 2008, t = 8
P(8) = 10,100 * (1 + 0.05)^8
P(8) = 10,100 * 1. 05^8
P(8) = 10,100 * 1.4774554437890625
= 14922.29
= 14,922
c) Use your function to estimate the year when the fox population will reach over 18,400 foxes. Round t to the nearest whole year, then state the year.
P(t) = A * (1 + r)^t
18400 = 10,100 * (1.05)^t
18400/10100 = 1.05^t
1.8217821 = 1.05^t
1.05^t = 1.8217821
In(1.05^t) = ln(1.8217821)
0.0487901 * t = 0.5998151
t = 0.5998151 / 0.0487901
t = 12.293787
Therefore eit will take 13 years
2000 + 13 = 2013
