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We have the following function:
So if we graph this function we will get the Figure below. Thus, let's study both the equation and the graph to get some conclusions. Therefore, we can assure these statements:
First. The function is defined only for
as shown in the Figure. This is also true because of 
where 
must be greater (or equal) than zero.
Second. The range of the function are the values of
.
Third. If creases then 
always creases, too.
So if we graph this function we will get the Figure below. Thus, let's study both the equation and the graph to get some conclusions. Therefore, we can assure these statements:
First. The function is defined only for
Second. The range of the function are the values of
Third. If
She should invest $6491.73.
The equation we use to solve this is in the form
,
where A is the total amount in the account, p is the principal invested, r is the interest rate as a decimal, n is the number of times per year the interest is compounded, and t is the amount of time.
A in our problem is 14000.
p is unknown.
r is 6% = 6/100 = 0.06.
n is 2, since it is compounded semiannually.
t is 13.
The equation we use to solve this is in the form
where A is the total amount in the account, p is the principal invested, r is the interest rate as a decimal, n is the number of times per year the interest is compounded, and t is the amount of time.
A in our problem is 14000.
p is unknown.
r is 6% = 6/100 = 0.06.
n is 2, since it is compounded semiannually.
t is 13.