SOLUTION: [ A mosquito population doubles every 7 days if there were 5 mosquitoes initially, after how many days will the population contain 80 mosquitoes? ] Thanks so much in advance:)

Question 824792: [ A mosquito population doubles every 7 days if there were 5 mosquitoes initially, after how many days will the population contain 80 mosquitoes? ]
Thanks so much in advance:)
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
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exponential growth:
y(t) = a * e^(kt)
where y(t) = value at time t
a = value at the start
k = rate of growth (when k>0) or decay (when k<0)
t = time
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200% of any initial amount will be present after 7 days:
arbitrarily choose 1 as the initial amount.
---
y(7) = 200 = 100 * e^(k7)
2/1 = e^(k7)
2 = e^(k7)
ln(2) = ln(e^(k7))
0.693147180559945 = k7
k = 0.693147180559945/7
---
k = 0.099021025794278
---
y(?) = 80 = 5 * e^(kt)
80 = 5 * e^(kt)
16 = e^(kt)
ln(16) = ln(e^(kt))
2.772588722239781 = kt
t = 2.772588722239781/k
t = 28
---
answer:
the population will grow from 5 to 80 mosquitoes in 28 days
---
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---
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