The population of Clover county doubles every 11 years. If the original population was 140,000 how many people will live in Clover county in 15 years?

Step-by-step 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