The population of a colony of mosquitoes obeys the law of un

The population of a colony of mosquitoes obeys the law of uninhibited growth. If there are 1000 mosquitoes initially and there are 1400 after 1 day, what is the size of the colony after 2 days? How long is it until there are 40,000 mosquitoes? What is the size of the colony after 2 days? How long is it until 40,000 mosquitoes are in the colony?

Solution

the population of mosquitoes is growing exponentially

applying the exponential growth formula

p = po e^rt

where , p is the final population

po = intital population

r is the rate of increase

t is the time period

plugging the values in the formula we get

1400 = 1000 e ^ r

r ln e = 1400/1000

r = .3364

now size after 2 days is

p = 1000 e^(.3364*2)

p = 1960 mosquitoes approximately

time it takes to become 40,000

40,000 = 1000 e^(.3364*t)

40 = e^(.3364*t)

ln 40 = .3364t

t = ln 40 / .3364

t = 11 days approximately