Answer:
The population for the first year is 75.35.
Step-by-step explanation:
Solution:
Given Data;
Carrying capacity (K) = 100
Growth rate (r) = 1.8% = 0.018
Initial population (Po) = 75
time = first year
Population at any given time (pt) = ?
Using the population growth rate formula, we have
<h2>
dp/dt = rp (1-p/t)---------------------------1</h2>
Where r is the growth rate, t is the given time and p is the population growth
Equation 1 is differentiated and is obtained as;
<h2>Pt = K/ [1 + (K-Po/Po)e^-rt]------------2</h2>
Substituting into equation 2, we have
Pt = 100/[ 1+ (100-75/75) *e^-0.018*1]
Pt = 100/[1+ (0.333 * e^-0.018]
= 100/[1 +(0.333*0.982)]
= 100/[1 + 0.327]
= 100/1.327
=75.35
