You are on a 9.7-mile run and have already run 7.85 miles. How many more miles do you need to run?
1 answer:
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Answer:
<em>It will take 14 years before the investment triples</em>
Step-by-step explanation:
<u>Continuous Compounding</u>
Is the mathematical limit that compound interest can reach if it was calculated and reinvested into an account's balance over a theoretically infinite number of periods.
The formula for continuous compounding is derived from the formula for the future value of a compound interest investment:
Where:
FV = Future value of the investment
PV = Present value of the investment
i = Interest rate
t = Time
It's required to find the time for an investment to triple, that is, FV = 3 PV, knowing the interest rate is i=8%=0.08.
Substituting the known values:
Dividing by PV:
Taking logarithms:
Solving for t:
t = 13.7 years
Rounding up:
It will take 14 years before the investment triples
Answer:
base = 5 m
Step-by-step explanation:
The area (A) of a triangle is calculated using the formula
A = bh ( b is the base and h the height )
here h = 3b + 1 ( 1 m greater than 3 times the base ), hence
A = b(3b + 1) = 40
Multiply both sides by 2
b(3b + 1) = 80 ← distribute and rearrange
3b² + b - 80 = 0 ← in standard form
Consider the factors of the product of the coefficient of the b² term and the constant term which sum to give the coefficient of the b- term
product = 3 × - 80 = - 240 and sum = 1
The factors are - 15 and + 16
Use these factors to split the b- term
3b² - 15b + 16b - 80 = 0 ( factor the first/second and third/fourth terms )
3b(b - 5) + 16(b - 5) = 0 ← factor out (b - 5)
(b - 5)(3b + 16) = 0
Equate each factor to zero and solve for b
b - 5 = 0 ⇒ b = 5
3b + 16 = 0 ⇒ b = -
However, b > 0 ⇒ b = 5
The base of the triangle is 5 m