00:01
In this question, the performance p of t, a function of a learner, is given as m minus c e to the power minus k t.
00:16
Now if we want to find an expression here for p, we can rearrange this equation as c e to the power minus k t is equal to m minus p.
00:28
Therefore e to the power minus k t is equal to m minus p upon c now taking natural logarithm on both sides we will get ln of e to the power minus k t is equal to ln of m minus p upon c now on the left side this will become minus k t and ln of e is one and on the right side we will have ln of m minus p minus ln of c.
01:04
Therefore, t is equal to 1 upon k times if we multiply the negative sign inside, we have lnc minus ln of m minus p.
01:17
This is an expression for t in terms of p and the other constants.
01:26
Next in the question we are given an example of a performance function for a given learner where p of t represents the height he can jump and the function is given as 20 minus 14 e to the power minus 0 .024 t and it is said that if p of t is equal to 12 feet then we need to find how much t is.
02:06
Now to solve this we will put these values in the equation so we have 12 is equal to 20 minus 14 e to the power minus 0 .024 t.
02:19
On rearranging we will get 14 e to the power minus 0 .024 t is equal to 20 minus 12 which is 8.
02:30
Therefore e to the power minus 0 .0.
02:34
024 is equal to 8 upon 14.
02:38
Now if we take natural logarithm on both sides again, we will get on this side minus, okay, let us take ln of e to the power minus 0 .024t is equal to ln of 8 upon 14.
02:54
Now on the left side this will become minus 0 .024t and ln of e is 1.
03:02
And on the right side we have ln of 8 upon 14 now this value will be minus 0 .24 approximately so therefore p is equal to minus 0 .24 upon minus 0 .024 which is 10 months now this is an approximate value because as we calculated ln of 8 upon 14 is approximately or close to minus 0 .0 .0...