Mary's allowance is based on the amount of time that she spends practicing different activities each week. This week Mary spent
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
The statement above is represented in the figure below. We have plotted the focus, the directrix and the parabola. So we know that the parabola opens downward. We also know that:
Because this is true the equation of the parabola is:
So our goal is to find the value of
. Given that the parabola opens downward, then 
and from the figure:
Accordingly:
Finally, the right answer is <span>f(x) = − one sixteenth x2</span>
Because this is true the equation of the parabola is:
So our goal is to find the value of
Accordingly:
Finally, the right answer is <span>f(x) = − one sixteenth x2</span>