Julie will build a rectangular pen for her dog against a barn. A wall from the barn will form one side of the pen. She has 32 m
2 answers:
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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.
Part a)
a) The given function is
We let
Interchange x and y.
Solve for y;
Part b) The range of f(x) refers to y-values for which f(x) exists.
The range of f(x) is
This is because the function is within y=-3 and y=3.
c) The range of
is
The domain is -3≤x≤3
This is because the domain and range of a function and its inverse swaps.
Part d) The graph is shown in the attachment.
