# Population Growth over time

## Main Question or Discussion Point

i guess I am trying to find the relationship between population growth and time.

bacteria population is 1000 during time 0minutes.
bacteria p.: 2000 time: 30 minutes
bacteria p.: 4000 time: 60 minutes
bacteria p.: 8000 time: 90 minutes
bacteria p.:16000 time: 120 minutes

What is the equation for the relationship between the two?

symbolipoint
Homework Helper
Gold Member
Simple visual inspection of the ordered pairs indicates exponential growth. Your example begins with 1000 units, and doubles (multiplication by 2) every 30 minutes. Check your intermediate algebra book for the chapter or section on exponential growth.

You could also use a logarithmic equation as they are basically the same as exponential equations.

symbolipoint
Homework Helper
Gold Member
A clearer way to understand this population growth exercise is that your exponent is a whole number for every 30 minute time passage; this means something like n/30, where n is for minutes after zero-time. Further, this exercise is like a geometric sequence in which the first term is 1000. The common ratio is obviously 2 (but in fact the "exponent" needs a bit of adjustment if you wanted the first term to actually be 1000; do you know what this adjustment is?)

Note carefully, I say is "like" a geometric sequence. Not "is" a geometric sequence. In the given case, the independant variable can be continuous.

Last edited:
HallsofIvy
Homework Helper
i guess I am trying to find the relationship between population growth and time.

bacteria population is 1000 during time 0minutes.
bacteria p.: 2000 time: 30 minutes
bacteria p.: 4000 time: 60 minutes
bacteria p.: 8000 time: 90 minutes
bacteria p.:16000 time: 120 minutes

What is the equation for the relationship between the two?
The population doubles every 30 minutes.

P(0)= 1000.
P(30)= 1000(2)= 1000(230/30).
P(60)= 1000(4)= 1000(22)= 1000(260/30).
P(90)= 1000(8)= 1000(23)= 1000(290/30).
P(120)= 1000(16)= 1000(24)= 1000(2120/30).

so P(t)= ?