8 is 2/3 of what number?
2 answers:
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1) Final expression:
2) Final expression:
Step-by-step explanation:
1)
The first expression is
First, we remove the 2nd bracket by changing the sign of all the terms inside:
Now we group the terms with same degree together:
Now we solve the expression in each brackets:
So, this is the final expression.
2)
The second expression is
We apply the distributive property, so we rewrite the expression as follows:
Solving both brackets,
Now we group terms of same degree together:
And solving each bracket,
So, this is the final expression.
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Answer:
11.1 years
Step-by-step explanation:
The formula for interest compounding continuously is:
Where A(t) is the amount after the compounding, P is the initial deposit, r is the interest rate in decimal form, and t is the time in years. Filling in what we have looks like this:
We will simplify this first a bit by dividing 2000 by 1150 to get
To get that t out the exponential position it is currently in we have to take the natural log of both sides. Since a natural log has a base of e, taking the natual log of e cancels both of them out. They "undo" each other, for lack of a better way to explain it. That leaves us with
ln(1.739130435)=.05t
Taking the natural log of that decimal on our calculator gives us
.5533852383=.05t
Now divide both sides by .05 to get t = 11.06770477 which rounds to 11.1 years.