00:01
In this problem, we are given a function for the growth rate for a yeast culture in grams per hour.
00:06
If the starting culture weighs 2 grams, what will be the weight of the culture after t hours and after 8 hours? so essentially, we want to solve our differential equation here.
00:15
So we have that the rate of growth, w prime, is equal to 0 .2 times the exponential of 0 .1t in grams per hour.
00:27
Let's rewrite w prime as dw over dt.
00:31
It makes things a little bit more explicit.
00:36
What we want to do here is solve for the weight w by bringing all of our t terms to the right hand side.
00:49
Now, let's integrate both the left and right side of our equation.
00:53
So on the left, we will simply have our weight, and on the right, we want to integrate a constant times the exponential.
01:02
And this will simply give us 0 .2 times our same exponential divided by 0 .1 here, plus our integration constant c...