A bacterial colony doubles in 3 hours. How long does it take to increase 5-fold?

Question

Can you explain how to double first, THEN how to quintuple. Please spell it out, so I'll have examples for my other problems. Thx!

Answer 1

population: A * 2 ^ (t / 3)
population now (t = 0): A

we will find t such that population is 5A

A * 2 ^ (t /3) = 5A
2 ^ (t / 3) = 5
(t / 3) * ln (2) = ln (5)
t = 3 * ln(5) / ln (2)
t = 6.97 hours

Answer 2

OK. lets say you have a population of 10. If it doubles in 3 hours, then at 3 hours you will have a colony of 20. Yes?

Then if you have a colony of 20, it too will double in 3 hours.
So in 3 more hours you have a colony of 40.

Your question asks how long it takes to increase 5-fold.
That would be a populaiton of 10 becoming 50.

10 doubles to 20 - 3 hours
20 doubles to 40 - 3 more hours = 6 hours

Unfortunately to get populations not multiplied by two, you need some trigonometry.

This is the expression of growth that doubles
B is the beginning population
b is the final population
n is the number of generations required.

b = B x 2^n

Solve for n:

logb = logB + nlog2

n = logb - logB
log2

n = logb - logB
.301

Answer 3

2^x = 5
x log(2) = log(5)
x = log(5)/log(2) [any base]
x = .69897 / .30103 = 2.319 {doubling periods}

2.319 * 3 = 6.9658 hours


///// note ///
to "double"

2^1 = 2 {here "1" is the "doubling time period" }

to find the number of "doublings" required
2^x = 5 ... and solve for "x"

x = the number of "doublings"

Answer 4

if colony is x
in 3 hrs colony =2x
in next 3 hrs i.e after 6 hrs colony= 4x
9hrs=8x
12hrs=16x
15hrs=32x
soo on
5 fold=2^5=32
so it takes 15 hrs......

if n-fold=> ans=n*time

Answer 5

N = N0(2^(t/3))
N/N0 = 2^(t/3)
When N/N0 = 5
2^(t/3) = 5
(t/3)log(2) = log(5)
t = 3Log(5)/Log(2)
t ≈ 6.9658 hr.