00:01
So here in this question we are given the temperature of a cooling liquid over the time that can be modeled as the exponential function that is t of x is equals to 60 multiplied by the 1 divided by the 2 raised to the power x that is divided by 30 plus 20.
00:18
Where t is representing the temperature in degrees celsius and x is representing the elapsed time which is in minute.
00:27
X is the time elapsed time which is in minute and t from here is representing the temperature.
00:36
Don't be confused between the t and the x.
00:39
So from that let's simplify this equation.
00:44
In the first part of the question we have to draw the graph of the function.
00:53
So we are having this function in terms of t and time and temperature.
01:00
So let's say here the coordinates here the x is representing time and here y axis is representing the temperature.
01:12
So according to this function this function is basically in the term of the exponents.
01:19
So the graph for somewhat that type of function will be parabolic in shape.
01:25
So the graph from here is somewhat like half of this function is somewhat like this hence the answer to the part a.
01:35
Now in the part b of the question we have to using the graph we have to determine how long to take that temperature to reach at the value of 28 degrees celsius.
01:48
Basically we have to find out the value of x or the time where the temperature of that given equation the graph is 28 degrees celsius.
01:56
So we are having the equation that is t of x is equals to 60 multiplied by the 1 divided by 2 raised to the power x divided by the 30 plus 20...