Water is poured into the top half of a spherical tank at a constant rate. if w(t) is the rate of increase of the depth of the water, then w is:

W is concave up.

Step-by-step explanation:

We are filling a spherical tank starting at the top half (meaning it is fulled half initially) at a constant rate. So, the tank level will increase in proportion to the tank's diameter at a given height.

Since the area of the circle is π·r² , then W(t) will be an increasing curve of second degree.  

So, the curve for W(t) is concave up.  

Also, the tank level increases over time at a more rapid rate.

Hence, the graph of W is concave up.