Ascientist performed an experiment with a radioactive substance whose half-life is 22 min. the scientist will sketch a graph of the situation, where x represents the time since the scientist first measured the substance, and y represents the amount of radioactive substance remaining at that time. the scientist will only sketch the graph in the quadrant or quadrants for which it makes sense to. in which quadrant or quadrants will the scientist sketch the graph?

We are given

x represents the time since the scientist first measured the substance

so, initial quantity =x

y represents the amount of radioactive substance remaining at that time

half-life is 22 min

so, we can write function as

We can see that this is exponential function

and exponent is over 1/2

and x is initial quantity

and x  can not be negative

so, y also can not be negative

Since, both x and y are positive

so, this function lies on quadrant I...............Answer

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.