Math Question?

Question

The population of a strain of bacteria doubles every hour. Suppose there are 400 bacteria.

a) Write an equation to represent y, the number of bacteria after x half- lives. Hint start with y = ABx

b) How many bacteria are there after each time?

i) 5 hours ii) 12 hours

Answer 1

Firstly, lets consider the case of a single --rather than 400-- bacterium. Hour 0=1 bacteria; Hour 1= 2 bacteria; Hour 2= 4 bacteria; Hour 3= 8 bacteria.

This is no linear relationship -- it's an exponential relationship. If x= the number of hours passed, then this equation models the relationship:

2^ x = number of bacteria

("^" represents to the power of)

So, for 1 hour, 2^1=2.
For 2 hours, 2^2=4
3 Hours, 2^3= 8.

It seems to fit when we start off with a single bacteria. So, how do we scale this up to your 400 bacteria?

The equation now becomes: 400 * 2^x = y

(i) After 5 hours 400 * 2 ^5 = 12800
(ii) After 12 hours 400 * 2 ^12= 1638400

Answer 2

it is a gp x,2x,(2)^2x,(2)^3x........
after x half lives it will be {(2)^x}*x
b)after five hours {(2)^5}*x bcoz in every hour bacterias are increasing with x,2x,(2)^2x,(2)^3x........
after 12 hours {(2)^12}*x