Answer:
a)
b) grams
c) days
Step-by-step explanation:
a)
We are going to use separation of variables to solve.
Get all your t's to one side and your N's to opposing side.
Multiply both sides by :
Divided both sides by :
Integrate both sides:
The equivalent exponential form is:
Using law of exponents you can write this as:
is just a positive constant that I'm going to replace with K:
Applying the symmetric property of equality:
Applying the commutative property of multiplication:
K actually represents the initial amount of chemical substance since when plugging in 0 for t you get K for N, like so:
We are given at time 0 the amount of chemical substance,N, is K. They want us to represent this value with instead. So the exponential equation is:
b)
We are given at .
We are asked to find how much of the chemical substance, N, remains after 2 days. So we replace t with 2 in :
Put into calculator:
(this was rounded to the nearest tenths)
c)
The last part is asking for how many days will it take a initial 800 grams to go down to half of 800 grams.
We need to see the following equation:
Divide both sides by 800:
Reduce the fraction:
Convert to logarithmic form:
Divide both sides by -0.069:
Input into calculator: