Answer:
Step-by-step explanation:
Given
From the attachment, we have:
Required
Determine the area
Area is calculated as:
Open brackets
Answer: it will take 17.33 years to double.
Step-by-step explanation:
The formula for continuously compounded interest is
A = P x e^(r x t)
Where
A represents the future value of the investment after t years.
P represents the present value or initial amount invested
r represents the interest rate
t represents the time in years for which the investment was made.
e is the mathematical constant approximated as 2.7183.
From the information given,
P = 425
A = 2 × 425 = 850
r = 4% = 4/100 = 0.04
Therefore,
850 = 425 x 2.7183^(0.04 x t)
850/425 = 2.7183^(0.04t)
2 = 2.7183^(0.04t)
Taking ln of both sides, it becomes
Ln 2 = 0.04t ln 2.7183
0.693 = 0.04t
t = 0.693/0.04
t = 17.325
We know there were 21 vehicles so one of the equations is:
c+b=21
We can find the second equation with the other given information:
30b+4c=318
We can use manipulate the first equation then use substitution to solve the system:
c=21-b
We can plug this into the second equation:
30b+4(21-b)=318
30b+84-4b=318
26b+84=318
26b=234
b=9
Now we can plug this into one of the original equations to solve for c (the first equation is easier):
c+9=21
c=12
You can check your work by plugging the answers into the two equations:
12+9=21
21=21
(30)(9)+(4)(12)=318
270+48=318
318=318
There are 9 buses and 12 cars.
