Answer:
30% decrease is the answer
Answer:
Half-life of the goo is 49.5 minutes
191.7 grams of goo will remain after 32 minutes
Step-by-step explanation:
Let denotes initial and final mass.
According to exponential decay,
Here, t denotes time and k denotes decay constant.
So, half-life of the goo in minutes is calculated as follows:
Half-life of the goo is 49.5 minutes
So,
Put
Put t = 32 minutes
Direct computation:
Parameterize the top part of the circle by
with , and the line segment by
with . Then
Using the fundamental theorem of calculus:
The integral can be written as
If there happens to be a scalar function such that , then is conservative and the integral is path-independent, so we only need to worry about the value of at the path's endpoints.
This requires
So we have
which means is indeed conservative. By the fundamental theorem, we have