matlab, how do i write a statement that will give me time on xaxis from y=0.3

Question

x=[0:.01:10];
y=(x.^2).*(exp(-x));

plot(x,y), grid
y1=max(y);

xlabel('TIME');
ylabel('CONCENTRATION IN BLOOD');
title('CONCENTRATIN OF SUSTANCE IN BLOOD vs TIME');

fprintf('(a) The maximum concentraion is %f 
',y1)

That's my program, and I'm having trouble to write a statement that will give me the time at when y=0.3 please assist
thank you

Answer 1

One key issue here is that there are multiple points on your plot where y = 0.3. If you want to find all of them in a simple way, you can follow these steps:

• Subtract 0.3 from your vector y, so that the points you want to find become zero crossings.
• Find the indices in the above vector where there is a sign change.
• For the y values on either side of the zero crossings, compute the percentage of the difference between them at which the value 0.3 lies. This essentially performs a linear interpolation between the two points on either side of the zero crossing.
• Use the above percentage to find the corresponding value of x for the zero crossing.

And here's the code along with a plot to show the points found:

>> yDesired = 0.3;
>> index = find(diff(sign(y-yDesired)));
>> pctOfDiff = (yDesired-y(index))./(y(index+1)-y(index));
>> xDesired = x(index)+pctOfDiff.*(x(index+1)-x(index))

xDesired =

    0.8291    3.9528

>> plot(x,y);
>> hold on;
>> plot(xDesired,yDesired,'r*')
>> xlabel('x');
>> ylabel('y');