00:01
In this question, the coffee's temperature is given by the function f.
00:07
And we are told that the initial temperature is 95 degrees.
00:13
And we are given the rate of change of that temperature.
00:17
And we are asked to find the coffee's temperature after 10 minutes.
00:23
To do that, we need to integrate the function f prime because the integral and the derivative cancel each other and we are going to get the function f.
00:36
So to find f, we need to calculate the integral of 9 times 0 .7 to the power of t.
00:46
And that's going to be negative 9 times the integral of 0 .7 to the power of t.
00:55
And that's a table integral.
00:58
That's an integral of an exponential function, and it's going to be negative 9 times 0 .7 to the t, divided by ln of 0 .7.
01:09
Plus the constant of integration c.
01:14
To find that constant, we need to use the given initial condition, f of 0 equals to 95...