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# C3- Questions Help. watch

1. Hi, i was wondering if anyone could help me on some past C3 questions.

A radioactive substance is decaying exponentially. Initially its mass is 480g. Its mass, M grams, at a time t years after the initial observation is given by

M = 480e^(kt)

where k is a constant. When t = 330, the mass of the substance will be 240g.

(i) State the value of the mass whenn t = 660.
(ii) Determine the value of K.
(iii) Find the rate at which the mass will be decreasing when t = 200.
2. i. Use natural logarithms
ii. Rearranging algebra
iii. Rearranging and using t=200
3. (i) Half life remember. Since 330 seconds is the half life of the substance then 480 - 240 - ???. Remember any 'state' questions don't need any working out and are awarded 1 mark most of the time.
(ii) Put t=330, M=240 and solve
(iii) Put t=200 and solve. With this value of M, 480-M/200 (I think) to find the rate
4. (Original post by Brianstorm91)
i. Use natural logarithms
ii. Rearranging algebra
iii. Rearranging and using t=200
dont u have to part ii first inorder to do part i.
5. i) 240 = 480e^(kt)

1/2 = e^(330k)

ln .5 = 330k

k= ln.5 / 330

ok? then plug in the values 660, and k

iii) find the derivative, this is the "rate", now plug in 200 into 't'. Done.
6. (Original post by Student#1)
i) 240 = 480e^(kt)

1/2 = e^(330k)

ln .5 = 330k

k= ln.5 / 330

ok? then plug in the values 660, and k

iii) find the derivative, this is the "rate", now plug in 200 into 't'. Done.
for the last part do you mean dM/dt for the derirative?
7. (Original post by TSR King)
for the last part do you mean dM/dt for the derirative?
Yes.
8. (Original post by Student#1)
Yes.
I still cant manage part iii, can some one go through it please?
9. (Original post by TSR King)
I still cant manage part iii, can some one go through it please?
you need to find dM/dt (think differentiation) and then sub t=200.
10. (Original post by GHOSH-5)
you need to find dM/dt (think differentiation) and then sub t=200.
so would dM/dt = t480e^kt

and then putting t=200.. you get 63070.86851, is that correct?
( k = (ln0.5)/330 )
11. (Original post by TSR King)
so would dM/dt = t480e^kt

and then putting t=200.. you get 63070.86851, is that correct?
( k = (ln0.5)/330 )
dM/dt is not t480e^kt, but something else. close, but not quite.
12. (Original post by GHOSH-5)
dM/dt is not t480e^kt, but something else. close, but not quite.
o yeh its k480e^kt... which gives me: -0.662.. correct?
13. (Original post by TSR King)
o yeh its k480e^kt... which gives me: -0.662.. correct?
yeh that's right for dM/dt, and i got the same after plugging it into my calc.
14. (Original post by GHOSH-5)
yeh that's right for dM/dt, and i got the same after plugging it into my calc.
beautiful.
15. (Original post by TSR King)
beautiful.
16. (Original post by GHOSH-5)
Thanks for the help.. Here's another question as i hate functions..

g: x |-> |x-2|
f: x |-> 5e^(0.5x) - 6.

(i) Determine the range of f and g.
17. (Original post by TSR King)
Thanks for the help.. Here's another question as i hate functions..

g: x |-> |x-2|
f: x |-> 5e^(0.5x) - 6.

(i) Determine the range of f and g.
g(x): think about what the moduli actually 'do'
f(x): think about the range of e^x and adapt it to this question. (hint: the 5 and the 0.5 don't really make much difference to the range)
18. (Original post by GHOSH-5)
g(x): think about what the moduli actually 'do'
f(x): think about the range of e^x and adapt it to this question. (hint: the 5 and the 0.5 don't really make much difference to the range)
would the range of g be x>2
19. (Original post by TSR King)
would the range of g be x>2
not exactly. counterexample x=2
20. (Original post by GHOSH-5)
not exactly. counterexample x=2
x > 0

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