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 16001600 after 1 day, what is the size of the colony after 44 days? How long is it until there are 40 comma 00040,000 mosquitoes? What is the size of the colony after 44 days? Approximately nothing mosquitoes. (Do not round until the final answer. Then round to the nearest whole number as needed.)

Solution

initial population = 1000

after 1 day population = 1600

population after 44 days

A = Ao e^kt

plugging the values

1600 = 1000 e^ (k *1)

finding k

1600 / 1000 = e^ (k *1)

ln (1.6) = k

k = .47

population after 44 days

A = 1000 e^ (.47* 44)

A = 957656775673 ( population after 44 days )

time takes until there are 40,000 mosquitoes

40,000 = 1000 e^ (.47t)

ln ( 40) / .47 = t

t = 7.84

approximately 8 days it takes until there are 40,000 mosquitoes