Question

A colony of bacteria grows at an exponential rate according to the function
P(t) = 2250e0.11t which describes the number of bacteria P at time t (in hours).

Find the following:
(A) Find the number of bacteria at t = 0 hours.
number of bacteria =

(B) Find the growth rate of the colony. Round your answer to two decimal places.
growth rate =

(D) When will the population double?
Round your answer to one decimal place.
time = hours

(E) At what time will the population reach 7000?
Round your answer to one decimal place.
time = hours

Answer 1

@Cosmichaotic

Answer 2

@kropot72

Answer 3

\[\large P(t) = 2250e^{0.11t }\]

Answer 4

Find the number of bacteria at t = 0 hours
\[\large P(0)=2250\]

Answer 5

divide?

Answer 6

no dear that is the answer

Answer 7

Write 2250e0.11t as 2250e^0.11t
Remember Alyygirl, the ^ makes ALL the difference?

Answer 8

for what d?

Answer 9

lets go slow

Answer 10

ok

Answer 11

\[\large P(t) = 2250e^{0.11t }\] is what you are given right?

Answer 12

yes

Answer 13

(A) Find the number of bacteria at t = 0 hours.
that means
\[P(0)\] and
\[P(0)=2250e^{0}=2250\]

Answer 14

ok so far?

Answer 15

ok so a is 2250

Answer 16

yes

Answer 17

yea

Answer 18

(B) Find the growth rate of the colony. Round your answer to two decimal places.

Answer 19

that is the number in the exponent before the \(t\) \[\huge P(t)=2250e^{\color{red}{0.11}t}\]

Answer 20

i do not see a part C

Answer 21

yea i already solved

Answer 22

(C) Find the population after 10 hours.
population = 6759

Answer 23

(D) When will the population double?
\[\large e^{.11t}=2\] solve for \(t\) do you know how?

Answer 24

2 times .11 squared?

Answer 25

To solve for t you must take the log of both sides and apply the log rule to bring the t out in front right?

Answer 26

rewrite in equivalent logarithmic form as
\[.11t=\ln(2)\]

Answer 27

then divide both sides by \(.11\)

Answer 28

@satellite73 help me

Answer 29

well then .11 cancels out

Answer 30

divide by 2?

Answer 31

right and your answer is
\[t=\frac{\ln(2)}{.11}\] whatever that is

Answer 32

@alyygirl i sense you are confused by this
lets back up a second

Answer 33

what about the 1?

Answer 34

whats is this for d