Answer:
Explanation:
Let the equation of the total population over the year be expressed as
P(t)= P0e^kt
P0 is the initial population
k is the constant of proportionality
t is the time
If the population of Clover county doubles every 11 years, this means that:
at t = 11, P(t) = 2P0
Substitute
2P0 = P0e^k(11)
2 = e^11k
ln2 = lne^11k
ln2 = 11k
k = ln2/11
k = 0.0630
If the original population was 140,000, we are to find the number of people that will live in Clover county in 15 years?
p0 = 140,000, k = 0.0630, t = 15 p(15) = ?
Substitute
P(t)= P0e^kt
p(15) = 140,000e^( 0.0630)(15)
p(15) = 140,000e^0.945
p(15) = 140,000*2.5728
p(15) = 360,193.87
Hence approximately 360,193 will live in clover country in 15years