A colony of bacteria grows exponentially. The colony begins with 8 bacteria, but 7 hours after the beginning of the experiment, it has grown to 720 bacteria.

1a. Give a formula for the number of bacteria as a function of time
i got P(t) = 8(1.90)^(t/7), i divided 720/8 got 90 and did 90/100 for the percentage of growth value and thought it was 1.09, but its wrong

Question

A colony of bacteria grows exponentially. The colony begins with 8 bacteria, but 7 hours after the beginning of the experiment, it has grown to 720 bacteria.

1a. Give a formula for the number of bacteria as a function of time
 i got P(t) = 8(1.90)^(t/7),  i divided 720/8 got 90 and did 90/100 for the percentage of growth value and thought it was 1.09, but its wrong

anonymous · Answer

please help

anonymous · Answer

Help please

myininaya · Answer

so at time t0=0, P(t0=0)=8
at time t7=7, P(t7=7)=720
one sec i brb

myininaya · Answer

are you still there?

myininaya · Answer

if you are...
since we have an exponential thing going on
we have something in this form P(t)=ab^t
to find what a and b are we know two points on the curve
(0,8)
and
(7,720)

myininaya · Answer

P(0)=ab^(0)=a1=a=8 since P(0)=8
so P(t)=8*b^t
P(7)=8*b^(7)=720 since P(7)=720 we can solve this equation for b
so we have 8b^7=720
                   b^7=720/8=90
                   b=90^(1/7)
so P(t)=8*90^(t/7)