exponential growth?

Question

culture of bacteria increases exponentially. monday theres 2000 per square inch, wednesday theres 4500.
what would be the general equation for this problem?
i have (2000)(.75)^ # of days
i divided 4500 by 2000- and divided that by 3 days-- and got .75...
but its wrong... what did i do wrong?

Answer 1

The fuction should be like number =2000*a^x where x is the number of days
Between Monday and wednesday there are two day so you know

4500 = 2000 a^2 so a^2 = 45/20 and a = sqrt(45/20)= 1.5

so N = 2000*(1.5)^x
If you considerer that there are trhee days the method would be alike

Answer 2

you didn't use the exponential function,e, that's what went wrong.

general equation for the number of Bacteria as a function of time is:

B(t) = (Bo)e^rt

where Bo is the initial amount

r is the rate

t is the time

use B(2) to determine the rate, r:

4500 = 2000e^2r

2r = ln(4500/2000)

r = 0.811/2

r = 0.41

so the equation is:

B(t) = 2000e^(0.41t)