The area of the entire figure below is 1 square unit. What is the area of the striped rectangle?
2 answers:
You might be interested in
Answer:
The initial mass of the sample was 16 mg.
The mass after 5 weeks will be about 0.0372 mg.
Step-by-step explanation:
We can write an exponential function to model the situation.
Let the initial amount be A. The standard exponential function is given by:
Where r is the rate of growth/decay.
Since the half-life of Palladium-100 is four days, r = 1/2. We will also substitute t/4 for t to to represent one cycle every four days. Therefore:
After 12 days, a sample of Palladium-100 has been reduced to a mass of two milligrams.
Therefore, when x = 12, P(x) = 2. By substitution:
Solve for A. Simplify:
Simplify:
Thus, the initial mass of the sample was:
5 weeks is equivalent to 35 days. Therefore, we can find P(35):
About 0.0372 mg will be left of the original 16 mg sample after 5 weeks.
Our P = 100, r = .08, n = 1 (annually means once a year), and t = 15. Filling in accordingly, we have 
. Simplifying a bit gives us 
and 
. Raising that number inside the parenthesis to the 15th power gives us 
. Multiplying to finish means that A(t) = $317.22