Posted by **Smartypants** on Saturday, June 18, 2011 at 1:23am.

The table below shows the number of molecules in experiment B.

Time(h) : 1st , 2nd , 3rd , 4th , 5th

No. of molecules : 3 , 8 , 15 , 24, 35

(i) how many molecules will there be in nth hour?

(ii) from which hour onwards would the no. of molecules be in experiment B?

- Math -
**Damon**, Saturday, June 18, 2011 at 5:59am
I tried an exponential and that did not work so try a polynomial:

change in n per hour 5 7 9 11

change in change in n per hour = 2

constant second derivative --> parabola

n = a + k t + c t^2

dn/dt = k + 2 c t

d^2n/dt^2 = 2 c

so

2c = 2

c = 1

and

n = a + k t + t^2

when t = 1, n = 3

3 = a + k + 1

a + k = 2

when t = 2, n = 8

8 = a + 2 k + 4

a + 2 k = 4

subtract those 2 equations

-k = - 2

k = 2

so

n = a + 2 t + t^2

when t = 3, n = 15

15 = a + 2(3) + 9

a = 0

so

n = + 2 t + t^2

check when t = 5

n = 10 + 25 = 35 check

so I claim that

n = 2 t + t^2

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