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# question core 3 watch

1. The mass of a substance is decreasing exponentially. Its mass now is 150 grams and its mass, m grams, at a time t years from now is given by m = 150e^–kt, where k is a positive constant. Find, in terms of k, the number of years from now at which the mass will be decreasing at a rate of 3 grams per year.

dm/dt = -150ke^-kt
3/-150k = e^-kt
ln(2/-150k) = lne^-kt
ln(2/-150k) = -kt
ln(2/-150k) / -k = t

the mark scheme says that the answer is :
-1/k ln(1/50k)
or
1/k ln(50k)
or
ln50 + lnk/k

how do i end up with any of the above and where have i gone wrong in my working out??
2. (Original post by elvss567)
The mass of a substance is decreasing exponentially. Its mass now is 150 grams and its mass, m grams, at a time t years from now is given by m = 150e^–kt, where k is a positive constant. Find, in terms of k, the number of years from now at which the mass will be decreasing at a rate of 3 grams per year.

dm/dt = -150ke^-kt
3/-150k = e^-kt
ln(2/-150k) = lne^-kt
ln(2/-150k) = -kt
ln(2/-150k) / -k = t

the mark scheme says that the answer is :
-1/k ln(1/50k)
or
1/k ln(50k)
or
ln50 + lnk/k

how do i end up with any of the above and where have i gone wrong in my working out??
The mass is decreasing so is negative.
3. (Original post by NotNotBatman)
The mass is decreasing so is negative.
so -3 instead of 3? is the rest of the working out allright?
4. (Original post by elvss567)
so -3 instead of 3? is the rest of the working out allright?
Yes and yes.
5. (Original post by NotNotBatman)
Yes and yes.
thankyou

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