Answer:
The oil slick area A exhibits exponential growth. Assume time t is measured in days.
dAdt=kA,A0=20,A1=20×3=60
Solve this separable differential equation.
dAdt=kA
∫dAA=∫kdt⟺ln(A)=kt+C
A(t)=A0ekt
Determine the constant k using the initial and first day oil slick area values A0,A1.
A1=A0ek×1 on day one
k=ln(A1A0)=ln(6020)=ln(3)
Substitute the known constant k and A0 into the equation.
A(t)=20eln(3)t
Verify the model A(t) matches the desired oil slick expansion. Does it triple every day?
A(0)=20e0=20
A(1)=20eln(3)1=60=3×20
A(2)=20eln(3)2=180=3×60
A(3)=20eln(3)3=540=3×180
It checks out!
On what day has the oil slick reached 1 hectare? The area is measured in square meters.
1 hectare = 10,000 square meters
10000≤20eln(3)t Solve for t days.
t≥1ln(3)ln(1000020)
t≥5.657 days
Answer
The oil slick reached 1 hectare after about 5+1/2 days.
Step-by-step explanation:
