Here’s the presentation I’d like you to run through before the lesson on Weds.
And here’s the one on modulus functions from today just in case!
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Mr Brewin’s Y13 – Transforming Functions24 comments to Mr Brewin’s Y13 – Transforming Functions |
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Hi
im really stuck on question 1c and 2c for the exponentials and logs special exam questions homework.
for question 1c:
i am getting two positive numbers for f(3) and f(4). This is the case when ive used both y = f(x) and y = f-1(x) (<– am i right in thinking that the later equation should be used in this question)
for question 2c:
i have tried it so many times but i cant seem to get it. maybe the formula im using is wrong:
3 = 10e^(-1/8 t) + 10e^(-1/8 (t +5))
?
I hope that makes sense… :/
Please may i have some help!!
Jacynth
Hi Jacynth,
Where are these questions from? You’ll need to give me a reference or type out the question for me to be able to help you.
Tea Lady
Is Q2c solve that equation? Is the answer t=2.316?
Just out at the moment J but will reply later or early tomorrow!
the questions are from the computer programme that selects exam questions for specifc topics.
For question 1c:
f: x = e ^ (x-2) – 1
Prove that the equation f(x) = x has a root in the interval (3,4)
For question 2c:
The amount of a certain type of drug in the bloodstream ‘t’ hours after it has been taken is given by the formula
x = De^(-1/8 t)
A dose of 10mg of the drug is given
A second dose of 10mg is given after 5 hours
No more doses of the drug are given. At time T hours after the second does is given, the amount of the drug in the bloodstream is 3 mg.
Find the value of T
Is the formula ive mentioned above correct for this question?
Thank you
Hi Jacynth,
Formula is correct except that you should have T not t.
I make it 2 hours 19 minutes.(rounded)
For 1(c)
If f(x) = x
then you need to work out f(x) – x
ie f(3) – 3
and f(4) – 4
which does give a sign change.
JT
ok great! Thanks very much!
Jacynth
Hi Jacynth,
Spotted the mistake in our first method!
Factorise out the e^-T/8 and move bracket to other side BEFORE taking logs, then it works.
JT
Mrs Tibble, may I have some help too please?
I am stuck on the same one as Jacynth at the moment – Q2)
Hi Natania,
Is this the drug in the bloodstream question? How far have you got with it?
Tea Lady
Don’t ask for help and then disappear!!!!
Indeed!
I think I have managed to do part a) but I’m not getting the right answer for part b). For 2c) I’ve got the equation that Jacynth got but after playing about the logs, I don’t think I’m getting anywhere.
OK. There is another way to do this question which is easier on the logs.
Take your answer to part (a) and add 10mg for the second dose. This gives you a new start value of 15.353mg. Zero the clock and time from the second dose. New constant will be 15.353 and t=T so you won’t have to worry about adding 5. Crunch the numbers and it works: T=13.1 hours I think.
Hope that helps.
Apologies, Mrs Tibble for not refreshing the page!
Brilliant! I’ve now got answer to 2b) now for 2c)
Thought that was 2c lol!
It gave me the answer to 2b)!
But I think I can use some of the same numbers in 2c) as well
Hmmm…
I’m still baffled by Q2c)!
What does 2c ask?
The amount of a certain type of drug in the bloodstream t hours after it has been taken is given by the formula
x = De^-1/8t
where x is the amount of the drug in the bloodstream, and D is the dose
no more doses are given. at time T hours after the second dose is given, the amount of the drug in the bloodstream is 3 mg.
c) find the value of T
That’s the one I did for you above!!
When t=0, x=10, so that will give you D (a constant)
Ah! I see it now! Thank you!
Phew!