00:01
Hi there, so for this problem, we are told that if c in units of 10 to the minus 4 molar is the concentration of glucose in a solution, then equally bacteria in the solution grow at a rate art in cell divisions per hour.
00:18
That is given by the following expression, that is that the rate capital art is equal to, well, we have.
00:32
In the denominator 0 .22 and this plus c and in the numerator we have 1 .35 times c and then this is cell divisions per hour so for part a of this problem we are asked about to find the growth rate of bacteria growing in 4 times 10 to the minus 4 molar glucose solution so the value that we're given for c is 4 times 10 to the minus 4.
01:14
But consider that in this case, we are told that c is in units of 10 to the minus 4.
01:23
So we are already accounting for the 10 to the minus 4.
01:28
So we don't need to include that.
01:30
So we just need to evaluate the function that we are given at this value.
01:34
So that will be 0 .22 plus 4.
01:38
4.
01:40
And in the numerator we have 1 .35 times 4.
01:46
So using our calculator, we obtain a value of 1.
02:00
So let me see, we are told to run your answer to 4 decimal places.
02:06
So that will be 1 .2 ,700 and 96.
02:16
And the answer for the units, it should be cell divisions per hour.
02:30
Yes, cell divisions per hour.
02:40
Let me put it in here.
02:41
Cell divisions and this hour.
02:55
So that's a solution for the first part of this problem.
02:58
Now for part b, we are asked about to find the derivative of this function with respect to c.
03:08
Okay.
03:10
So to find the derivative of this, we will have the derivative of equation.
03:18
So when we have that, we just simply start with the derivative of the numerator.
03:26
So that will be the derivative of 1 .35 times c...