C3 differentation question
i need help with this question.
For a certain part of its flight, the height h metres of a balloon after t seconds can be modelled by
h = 100 + 200e–0.01t.
(a) (i) Find an expression for t in terms of h.
(ii) Find the time when the height of the balloon is 150m.
For a certain part of its flight, the height h metres of a balloon after t seconds can be modelled by
h = 100 + 200e–0.01t.
(a) (i) Find an expression for t in terms of h.
(ii) Find the time when the height of the balloon is 150m.
oh and part b as well
Find an expression for dh/dt and its value when t = 150. Explain the significance of your answer in the context of the model.
Find an expression for dh/dt and its value when t = 150. Explain the significance of your answer in the context of the model.
a)i) is simply algebraic rearrangement
a)ii) is simply value substitution
b) is a matter of exponential differentiation
It shouldn't be too tricky, especially not a. See where you get with these starting clues.
a)ii) is simply value substitution
b) is a matter of exponential differentiation
It shouldn't be too tricky, especially not a. See where you get with these starting clues.
for the dh/dt then got that but i'm not sure what or how to explain it. and for the first part i have done (i) but not sure about the answer for (ii)
Original post by whovian_2297
for the dh/dt then got that but i'm not sure what or how to explain it. and for the first part i have done (i) but not sure about the answer for (ii)
`For ii it is just substituting into your original equation. h=150, and you are finding t, so just rearrange to find t.
Original post by aoxa
`For ii it is just substituting into your original equation. h=150, and you are finding t, so just rearrange to find t.
But for the answer i got a answer of 13863...
Original post by whovian_2297
for the dh/dt then got that but i'm not sure what or how to explain it. and for the first part i have done (i) but not sure about the answer for (ii)
Just a matter of substituting the given value of h.
As for the explanation, I don't know what the relevance would be without working out a value. But, you might want to try considering the signage and zero/non-zero nature of your value - it might well be something to do with turning points in the trajectory. It might instead be asking you something more fundamental about the exponential nature of the model.
Just try to see what you can infer from your own answer
Original post by whovian_2297
But for the answer i got a answer of 13863...
Have you written the question down correctly? It seems slightly odd that e is just being used as a constant without any exponentiation involved here.
Original post by sjgriffiths
a)i) is simply algebraic rearrangement
a)ii) is simply value substitution
b) is a matter of exponential differentiation
It shouldn't be too tricky, especially not a. See where you get with these starting clues.
a)ii) is simply value substitution
b) is a matter of exponential differentiation
It shouldn't be too tricky, especially not a. See where you get with these starting clues.
I dont think it's exponential differentiation as there is no "t" constant on e. For some reason I just get -0.01 :/
Original post by sjgriffiths
Just a matter of substituting the given value of h.
As for the explanation, I don't know what the relevance would be without working out a value. But, you might want to try considering the signage and zero/non-zero nature of your value - it might well be something to do with turning points in the trajectory. It might instead be asking you something more fundamental about the exponential nature of the model.
Just try to see what you can infer from your own answer
As for the explanation, I don't know what the relevance would be without working out a value. But, you might want to try considering the signage and zero/non-zero nature of your value - it might well be something to do with turning points in the trajectory. It might instead be asking you something more fundamental about the exponential nature of the model.
Just try to see what you can infer from your own answer
ah ok thank you
Original post by whovian_2297
But for the answer i got a answer of 13863...
Yes, 13863 seconds
Original post by aoxa
Yes, 13863 seconds
ah i completely forgot it was in seconds, that's why it seemed odd
Original post by sykik
I dont think it's exponential differentiation as there is no "t" constant on e. For some reason I just get -0.01 :/
Yeah, that would be right.
It makes me wonder if the question is actually correct; it seems unusual that e is merely being used independently to any variable.
(edited 9 years ago)
Original post by sykik
Lol for part ii i got 49365 seconds... is that correct?
hmm i'm not sure, what was the eqn you got after part a
Original post by sykik
i used my calculator to solve the equation
hmm then i'm no sure as i put 150 into my part A answer and got 13863
Are you sure the question wasn't this:
The equation as you write it is unusual for a C3 paper as it doesn't actually involve any exponentials, unless it's specifically trying to trick you (which I've never seen before).
The equation as you write it is unusual for a C3 paper as it doesn't actually involve any exponentials, unless it's specifically trying to trick you (which I've never seen before).
Original post by sjgriffiths
Are you sure the question wasn't this:
The equation as you write it is unusual for a C3 paper as it doesn't actually involve any exponentials, unless it's specifically trying to trick you (which I've never seen before).
The equation as you write it is unusual for a C3 paper as it doesn't actually involve any exponentials, unless it's specifically trying to trick you (which I've never seen before).
It is, i just forgot to put the ^ to show it as a power
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