babeeb0oL

babeeb0oL

Answered

2021-09-11

A fruit fly population of 24 flies is in a closed container. The number of flies grows exponentially, reaching 384 in 18 days. Find the doubling time (time for the population to double) and write an equation that models this scenario.

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Answer & Explanation

tafzijdeq

tafzijdeq

Expert

2021-09-12Added 92 answers

As we know,
Exponential growth of population is given by
A=Pert (1)
Here A is the population after t days, P is the initial population and r is the growth rate.
As given,
p=24
According to question,
Population becomes 384 in 18 days
Implies,
A=384
t=18 days
Equation becomes
384=24e18r
e18r=38424
Applying ln both sides
18r=ln(384)ln(24)
18r5.9513.178
⇒=0.1541
Put the value into equation (1)
A=Pe0.1541t
We have to find the doubling time
That is, put A=2P
2P=Pe0.1541t
2=e0.1541t
Applying ln voth sides
ln2=0.1541t
t=ln20.1541
=0.69310.1541
=4.4977
4
Hence the required doubling time is 4 days.

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