A.) P(t) = P0e^(kt)
P(20/60) = 40 e^(20k/60)
80 = 40 e^(k/3)
e^(k/3) = 80/40 = 2
k/3 = ln(2)
k = 3ln(2)
b.) P(8) = 40(2)^24 = 40(16777216) = 671088640 cells
d.) Rate of change = e^(8k) = e^(8(3ln(2))) = e^(24ln(2)) = e^(16.6355) = 16777216 cells/hour
e.) P(t) = 40(2)^(3t); t in hours
1,000,000 = 40(8)^t
25,000 = 8^t
ln(25,000) = t ln(8)
t = ln(25,000)/ln(8) = 4.87 hours
Conclusion:
Please refer to the explanation provided.
Detailed explanation:
Starting with these facts:
Total revenue = $250
Fee charged = $70 per car
Tips received = $50
Equation 1 representing the above:
(Fee per car × number of cars) + tips = total revenue
Let the number of cars be c.
Thus, we have:
$70c + $50 = $250
Part B:
Total revenue = $250
Fee charged = $75 per car
Tips received = $35
Supplies cost per car washed = $5
Equation 2:
(Fee per car × number of cars) + tips - (supplies cost × number of cars) = total revenue
$75c + $35 - $5c = $250
$70c + $35 = $250
Part C:
Equation 1 does not factor in costs associated with washing the car, while equation 2 does incorporate costs, which are deducted from the amount charged per car. Additionally, tips in equation 1 total $50 compared to a $35 fee in equation 2.
Let's sketch the triangle.
The sides are a= 37.674 miles
b= 11.164 miles
c= 36.318 miles
We'll apply the cosine rule for angle calculations
(since the sine law cannot be employed without knowing any angle measurements).
The cosine law is given by
Substituting the values results in
C = 74.48°
We can find angle A using the sine law
A= 
A = 87.38°
The third angle B can be determined by calculating 180° minus the sum of angles A and C
B = 180 - 161.86
B = 18.14°
Thus, we have calculated all three angles (as shown in the attached figure).
