The store keeper sold 9 1/4 yards from a piece of material containing 53 yards. How much was left in the original piece?
2 answers:
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Answer:
Using the rule of 72, the doubling time is 9.35 years.
The exact answer is that the doubling time is 8.89 years.
Step-by-step explanation:
By the rule of 72, we have that the doubling time D is given by:
The interest rate is in %.
In our exercise, the interest rate is 7.7%. So, by the rule of 72:
.
Exact answer:
The exact answer is going to be found using the compound interest formula(since the rule of 72 is a simplification of this formula).
The compound interest formula is given by:
Where A is the amount of money, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit t and t is the time the money is invested or borrowed for.
So, for this exercise, we have:
We want to find the doubling time, that is, the time in which the amount is double the initial amount, double the principal.
There are 52 weeks in a year, so
Now, we apply the following log propriety:
So:
The exact answer is that the doubling time is 8.89 years.
Answer:
Step-by-step explanation:
In , notice the third term of the quadratic in standard form is formed entirely by
.
Therefore, in :
.
Now that we found , we must find
. The first term of the quadratic in standard form is formed entirely by
. Therefore:
.