Help with this exponential functions question plz... thnku!?

Question

If a bacteria population doubles in 5 days, when was it 1/2 of its present population?!

Solve this question using exponential functions and plz show how u did it.... thnk u!! =D

Answer 1

Let current population be P

Then in 5 days new population = 2P

Now for exponential growth:

Population = Ae^(kt) (where k = growth constant, A = constant and t = time in days)

When t = 0 (now), population = P
So P = Ae^(k.0) = A
Thus Population = Pe^(kt)

So P = 2P when t = 5

2P = Pe^(5k)

Therefore 2 = (e^k)^5
So e^k = 2*(0.2)

Thus Population = P.2^(0.2t)

When Population = ½P

½P = P.2^(0.2t)
So 2^(0.2t) = ½ = 2^(-1)
Thus 0.2t = -1
t = -5

Ie it was 5 days ago

Answer 2

if the population, p is double in 5 days
it means the population was half what it was 5 days!

Answer 3

it is clear that the answer is 5 days, but the mathematical soultions is:

ok........the equation is :
the future population=2^n

as n is the number of 5 days

So: F1=2^n1
F2=2^n2

but F2=2F1

so, dividing the two equations we have

F2/F1=2=2^(n1-n2)
so n1-n2=1

So, that was since 5 days

Answer 4

5 day = 2x
4 day = x
3 day = (1/2)x
2 day = (1/4)x
1 day = (1/8)x

ANS : Day 3