Question

A biologist is researching a newly-discovered species of bacteria. At time t = 0 hours, he puts two hundred bacteria into what he has determined to be a favorable growth medium. Eight hours later, he measures 1200 bacteria. Assuming exponential growth, what is the growth constant "k" for the bacteria? (Round k to three decimal places.

Answer 1

Lets use this formula for exponential growth
A= Pe^(kt)

A= Amount of Population ending
P = Population at start
e= e
k= growth constant
t = time

plugging in

1200 = 200e^(8k) divide both sides by 200
1200/200 =200e^(8k)/ 200 then take natural log both sides
ln(6) = 8k divide 8 both sides use cal and you should get your answer

Answer 2

@Princer_Jones i have no clue on how to solve this

Answer 3

ok. so do you know what is meant by exponential growth??

Answer 4

i showed all but the last steps

ok divide both sides by 8
ln(6)/8 = 8k/8
k = Ln(6)/8

on calculator punch in 6 and there should be a button for natural log Ln

ln6 = 1.79
1.79/8 = .22375/hr

Answer 5

@_ashleeey

Answer 6

ex growth is 2,4,8,16,32,64,128,256,512,1024,2048,4096....
or 2^2,2^3,2^4,2^5,2^6,2^7

the exponent grows and the growth doubles

Answer 7

http://en.wikipedia.org/wiki/Exponential_growth

Answer 8

@Princer_Jones no. i havent gotten the hang of this topic whatsoever

Answer 9

what about this one
A recent earthquake measured 6.8 on the Richter scale. How many times more intense was this earthquake than an earthquake that measured 4.7 on the Richter scale?

Answer 10

did you red the link I gave? It will take only 5 mins and then you see the solution @zpupster gave... If you have problem, then tell me,,.
@_ashleeey

Answer 11

*read

Answer 12

didnt see it, one sec.

Answer 13

Just read the definiton, and then tell me.

Answer 14

i read it

Answer 15

ok so the formula is
x(t)=x(0)*exp(kt) where k is the growth contant we need to calculate
x(0) the amount in time 0
and x(t) the amount in time t

Answer 16

@_ashleeey

Answer 17

right.

Answer 18

all the data are already provided
see x(0)=200
x(8)=1200
in the question

Answer 19

@_ashleeey

Answer 20

i see

Answer 21

so you can continue now i think, you just need to insert the values in the formula and calculate k

Answer 22

@_ashleeey

Answer 23

great, ill get to it, do you still have time?

Answer 24

yeah sure... @_ashleeey

Answer 25

A recent earthquake measured 6.8 on the Richter scale. How many times more intense was this earthquake than an earthquake that measured 4.7 on the Richter scale?

Answer 26

hi. @_ashleeey

Answer 27

do you have any idea of this problem??

Answer 28

ummmmm, im guessing some multiplication?

Answer 29

No i mean do you know how the Ritcher scale works, the formula relating its magnitude and intensity??

Answer 30

Nopee

Answer 31

read this then at first, or else the solution I will provide, will be of no use
http://www.sosmath.com/algebra/logs/log5/log56/log56.html

Answer 32

are you reading? .@_ashleeey

Answer 33

i read it

Answer 34

so so the formula is M= log (I/S) where M is the magnitue, I is the intensity and S is the intensity of a standard earth quake

Answer 35

right

Answer 36

@_ashleeey I posted the solution in the attachment. read it and tell me if you have ay problem

Answer 37

@Princer_Jones how come theres subtracting involved?

Answer 38

we subtracted to eliminate S, which is unknown here