The present value of a building in the downtown area is given by the function
p(t) = 300,000e^-0.09t+�ãt/2 f or 0 _< t _< 10
Find the optimal present value of the building. (Hint: Use a graphing utility to graph the function, P(t), and find the value of t0 that gives a point on the graph, (t0, P(t0)), where the slope of the tangent line is 0.
I see 3 postings of this same question by you.
Each time the symbols you want to create are not
coming out the way you intended.
Did you not click on your post to see what it looked like?
The reason you are not getting an answer is that we can't make out your equation.
I am concerned the part of
+�ãt/2 f
is that supposed to be a √ sign?
where does the f come in?
Yes Reiny you got the symbol right. I inserted it on MS Word, however when i posted it the symbol came out wrong. Thanks.
The f or 0 _< t _< 10
To find the optimal present value of the building, we need to find the value of t, denoted as t0, where the slope of the tangent line to the graph of the function is 0.
Step 1: Graph the function
To visualize the graph of the function, you can use a graphing utility or software. Enter the function into your graphing utility:
p(t) = 300,000e^(-0.09t + t/2)
Choose an appropriate x-axis or t-axis range, such as 0 to 10, to match the given domain.
Step 2: Find the point where the slope of the tangent line is 0
Look for the point on the graph where the slope of the tangent line is 0. This will correspond to the optimal present value of the building.
Locate the point (t₀, P(t₀)) where the graph has a horizontal tangent line. At this point, the slope of the tangent line will be 0.
Step 3: Read the value of t₀
Once you've located the point of interest, read the value of t corresponding to that point. This value will give you the optimal present value of the building.
Using this method, you can find the optimal present value of the building by graphically analyzing the function and identifying the point where the slope of the tangent line is 0.