The first step to determining the answer to this item is to calculate for the effective interest using the equation,
ieff = (1 + i/m)^m - 1
where ieff is the effective interest, i is the given interest and m is the number of compounding period.
Part A: m in this item is equal to 12.
Substituting,
ieff = (1 + 0.10/12)^12 - 1 = 0.1047
The amount of money after n years is calculated through the equation,
An = A(1 + ieff)^n
If An/A = 2 then,
2 = (1 + 0.1047)^n
The value of n is 6.96 years
Part B: For the continuously compounding,
An = Ae^(rt)
An/A = 2 = e^(0.10t)
The value of t is equal to 6.93 years.
Hence, the answers:
<em>Part A: 6.96 years</em>
<em>Part B: 6.93 years</em>
The area of the David's pantry = 10 square feet.
The length of the pantry = 5 feet.
<h3>Define the term area of the rectangle?</h3>
- The territory inhabited by a rectangle inside its 4 sides or limits is known as its area.
- The area of such a rectangle is determined by its sides. Essentially, the formula calculating area is equivalent to the product of the rectangle's length and breadth.
For the given question.
- David's kitchen is 60 square feet in size.
- The kitchen is six times the size of the living room.
Thus,
Area of kitchen = 6 x area of the pantry
60 = 6 x area of the pantry
area of the pantry = 60 / 6 = 10 square feet.
Area of the pantry = length x breadth
10 = length x 2
length = 10/2 = 5 feet.
Thus, the length of the pantry is found as the 5 feet.
To know more about the area of the rectangle, here
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sq. units.