8) A certain radioactive material decays at a rate proportional to the amount present.
Initially there is 50 mg of the material present. It is observed that the material has lost 10% of its original mass after 2 h. Find
(a) an expression for the mass of the material remainin at any time t, and
(b) the mass of the material after 4h
Ans 40.5 mg
PS: Only learnt seperable equation
9) A certain bacteria grow at a rate proportional to the number present. If the number of bacteria doubles in 4h, how many may be expected at teh end of 12h?
Ans 8 times
Again same type of qn.......
those are easy questions...when u read proportional......it already tells u the formula...all it needs is to put in all data n u get the answers.
try reading yer lecture notes again .there are 2 formulas, one for growth the other for decay...just use the right one n put in data n ya have d answer!
Hi,
Let x represent the amount of radioactive material (in mg) at time t (in hr).
Now dx/dt represents rate of change of x.
Given that rate is proportional to amount present, we use O-level knowledge (i.e., ratio, rate and proportion) to obtain
dx/dt = kx, where k < 0, since it is a decay (i.e. x decreases as t increases)
From here, we will apply the method of variable separable to find the general solution.
Since we are given some other information:
x = 50 when t = 0,
x = 0.9(50) when t = 2,
we will need to find the particular solution.
Thanks.
Cheers,
Wen Shih
wow what course is this sia.
wee_ws thanks again =]
got it
left got 10*, 11* and 12 * all star qns. Trying!
Originally posted by Wireless-:9) A certain bacteria grow at a rate proportional to the number present. If the number of bacteria doubles in 4h, how many may be expected at teh end of 12h?
Ans 8 times
Again same type of qn.......
This question is fairly simple. Don't need to read too much into it just to answer this question:
Let the initial amount of bacteria be x.
x doubles to 2x in 4 hrs.
2x doubles to 4x in 8 hrs.
4x doubles to 8x in 12 hrs.
Hence it is 8 times.
Simply put, x => 2x => 4x => 8x (with each arrow representing every 4 hrs that have passed)
I'm solving this in a very layman and simplistic way. So this may not be the proper working that your tutors might desire.
Ok the oni 1 left i dunno is this
11*) If the interest is compounded continuosly at a constant rate of 4% per annum, how long will it take a bank deposit tto double?
Let y be the amt of money in the bank at any time t (in years)
dy/dt=0.04y
(25/y)dy = 1dt
integrate
25ln|y|=t+K
y=e^([t/25]+K)
Then i dunno how to do
i donno if this works. but there is a formula that financial advisors use to calculate how long it takes to double a principle amount.
72/interest rate
=72/4 = 18years.
close 17.3 years is the ans.
Nid differential eqns working =/
Nvm finally got it. Should find the original amt 1st