Exercise
The temperature T in degrees Celsius of a chemical reaction is
given as a function of time t, expressed in minutes, by the function
defined on ¿ by: T (t )=(20 t +10)e−0.5t.
1) What is the initial temperature?
2) Show that T' (t )=(−10 t +15)e−0 .5t.
3) Study the sign of T' (t ), then draw up the table of variations of T
. We do not ask for the limit of T in +∞.
4) What is the maximum temperature reached by the reaction
chemical. We will give an approximate value to within 10−2.
5) After how long does the temperature T go back down
to its initial value? We will give an approximate value of this
time in minutes and seconds.
DM 2: study of a function
Exercise
The temperature T in degrees Celsius of a chemical reaction is
given as a function of time t, expressed in minutes, by the function
defined on ¿ by: T (t )=(20 t +10)e−0.5t.
1) What is the initial temperature?
2) Show that T' (t )=(−10 t +15)e−0.5 t.
3) Study the sign of T' (t ), then draw up the table of variations of T
. We do not ask for the limit of T in +∞.
4) What is the maximum temperature reached by the reaction
chemical. We will give an approximate value to within 10−2.
5) After how long does the temperature T go back down
to its initial value? We will give an approximate value of this
time in minutes and seconds.