Question

a tank holds 5000 gallons of water, which drains from the bottom of the tank in half an hour. The values in the table show the volume V of water remaining in the tank (in gallon) after t minutes.a) If P is the point (15,1275) on the graph of V, find the slopes of hte secant lines PQ when Q is the point on the graph with the following values.(5, 3410) -427/2(10, 2210) -187(20, 550) -145(25, 145) -113(30, 0) -85B) estimate the slope of hte tangent line at P by averaging the slopes of two adjacent secant lines. (Round your answer to one decimal places).

Answer 1

Answer:

• secant slopes: -213.5, -187, -145, -113, -85
• tangent slope: -166

Step-by-step explanation:

A) the slope values you have put in your problem statement are correct. As you know, they are computed from ...

  (change in gallons)/(change in time)

where the reference point for changes is P. Using the first listed point Q as an example, the secant slope is ...

  (3410 -1275)/(5 -15) = 2135/-10 = -213.5 . . . . gallons per minute

__

B) The average of the secant slopes for points Q adjacent to P is ...

  (-187 +(-145))/2 = -332/2 = -166 . . . . gallons per minute

The tangent slope at point P is estimated at -166 gpm.