Array of x and y values. Find value of y when x=0, how?

Hello. I have an assignment in school, where we got an array with x and y values to plot.

Time=[0.5:0.5:5];

A=[1.2 0.73 0.45 0.27 0.16 0.11 0.06 0.035 0.022 0.013];

plot(Time,A) gives me a graph but I need the value of A when Time=0;

I don't have a function or equation, only these values. So when Time=0, what is the value of A?

I'm thinking that some kind of y-intercept thing can be the solution?

Answer 1

[KL]

You might want to use interp1,

read: https://de.mathworks.com/help/matlab/ref/interp1.html

Hint: For your case, 0 lies outside the range you've got, so you might want to extrapolate.

[Elin Berntsson]

Okey great. But how do i extrapolate, didn't really understand matlabs explanation? Should i use "vq = interp1(v,xq,method,extrapolation)", in that case what does method mean?

[KL]

Quite close! Just scroll down that documentation page. It's your homework so it's nice to skim through that page to know how it works :)

https://de.mathworks.com/help/matlab/ref/interp1.html#input_argument_d119e519965

[the cyclist]

Be aware that this method is subject to the same issue that I comment on in my answer. The method of extrapolation will explicitly or implicitly make assumptions about the functional form underlying the data. The result you get will be highly dependent on those assumptions.

[Elin Berntsson]

Yeah so I've been trying a few times now but i don't think I'm using the interp1 function right.

this is my code so far:

Time=[0.5:0.5:5];

A=[1.2 0.73 0.45 0.27 0.16 0.11 0.06 0.035 0.022 0.013];

plot(Time,A)

A0 = interp1(A,0,linear,extrap)

it's not working and I still kinda don't understand the description that mathworks has for it.. Thankful for your help!

[KL]

I agree with the cyclist. In your question you say ...I don't have a function or equation, only these values... and looks like you do have one.

Answer 2

[the cyclist]

Strictly speaking, it is not possible to know what the value of A is at Time=0, given only this information. An infinite number of functions could fit these data, and give different values at Time=0. Or maybe Time=0 is an asymptote, and the fit line never crosses it.

Do you have any other relevant info that you have not shared?

[Elin Berntsson]

Well yes I have the two arrays of values, time and A(time). I also have an equation;

A(time)=A0*exp(-k*time)

I don't have a value for k, that is also something that i should calculate. The question says: Calculate A0 (value of A when the time=0) and k by plotting the values in the arrays;

Time=[0.5:0.5:5];

A=[1.2 0.73 0.45 0.27 0.16 0.11 0.06 0.035 0.022 0.013];

[the cyclist]

Fantastic.

If you take the log of each side of that equation, you get

log(A) = log(A0) - k*time

That's a linear equation that can be fit using the data you have, using the polyfit command.