The population triples ( P × 3 ) every ten minutes...
So if ten minutes is reached there will be 1,200 bacteria.
Edited - missed the question
** The units for time should be in minutes.
P = 400 × 3^(t/10)
at t = 0 ; P = 400
at t = 10 ; P = 1,200
When P = 600
600 = 400 × 3^(t/10)
6/4 = 3^(t/10)
Log(3/2) = Log(3^(t/10))
power rule
Log(3/2) = (t/10) Log(3)
10 × Log(3/2)/Log(3) = t
3.69 minutes the population will be at 600 bacteria
Unites for time are in minutes.
You have to do Rise over Run.
1.) Start at the origin
2.) go down to one of your points, (in this case the point in the 4th quadrant)
3.) Go down 6 units, then 3 units right
4.) The slope is 6/3 or 2/1
m=2/1
(6a+11)=(2a+83)
6a+11=2a+83
-11 -11
6a=2a+72
-2a -2a
4a=72
4/4a=72/4
a=18
The solution is 18
<u>Here are your fill-ins:</u>
r = 1 is a zero, so (r-1) is a factor.
r = -1 is a zero, so (r+1) is a factor.
The remainders from synthetic division are 0 each time.
See the attachment for the synthetic division numbers.
_____
The reduced quadratic is ...
... x² -6x +13 = 0
Solving by completing the square, we have ...
... (x -3)² = -4
... x = 3 ± 2i
_____
The quadratic formula would tell you ...
... x = (-(-6) ± √((-6)² -4(1)(13)))/(2·1) = (6±√-16)/2 = 3±2i
