SOLUTION: 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

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Question 1089276: 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 4 ​days? How long is it until there are 90,000 ​mosquitoes?
What is the size of the colony after 44 ​days?  

Approximately 3842 mosquitoes.
​(Do not round until the final answer. Then round to the nearest whole number as​ needed.)
How long is it until 90,000 mosquitoes are in the​ colony?
About ________ days.  
​(Do not round until the final answer. Then round to the nearest tenth as​ needed.)
I have the approximate mosquitoes but not the number of days???
Answer by josgarithmetic(39615) About Me  (Show Source):
You can put this solution on YOUR website!
y=1000%2Ae%5E%28kt%29
If y=1400 for t=1:
1000e%5E%28kt%29=1400
e%5E%28k%2A1%29=1.4
ln%28e%5Ek%29=ln%281.4%29
k=ln%281.4%29
k=0.3364

MODEL: highlight_green%28y=1000e%5E%280.3364t%29%29


How much time until y=90000?
90000=1000e%5E%280.3364t%29
90=e%5E%280.3364t%29
0.3364t=ln%2890%29
highlight%28t=13%29, to nearest whole number of days.