amos94CHAPTER 2 LIMITS AND DERIVATIVES2.1 Exercises1. A tank holds 1000 gallons of water, which drains from thebottom of the tank in half an hour. The values in the table showthe volume V of water remaining in the tank (in gallons) aftert minutes.t (min)51015252030V (gal)69428 0444250111(a) If P is the point (15, 230) on the graph of V, find the slopesof the secant lines PQ when Q is the point on the graphwith t 5, 10, 20 25, and 30.sdi b01(b) Estimate the slope of the tangent line at P by averaging theslopes of two secant lines.(c) Use a graph of the function to estimate the slope of thetangent line at P. (This slope represents the rate at which thewater is flowing from the tank after 15 minutes.)0A cardiac monitor is used to measure the heart rate of a patientafter surgery. It compiles the number of heartbeats after t min-tes. When the data in the table are graphed, the slope of theangent line represents the heart rate in beats per minute.01t1909

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Asked Oct 2, 2019
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I don't know understand one and it's parts.

amos
94
CHAPTER 2 LIMITS AND DERIVATIVES
2.1 Exercises
1. A tank holds 1000 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 gallons) after
t minutes.
t (min)
5
10
15
25
20
30
V (gal)
694
28 0
444
250
111
(a) If P is the point (15, 230) on the graph of V, find the slopes
of the secant lines PQ when Q is the point on the graph
with t 5, 10, 20 25, and 30.
sdi b
01
(b) Estimate the slope of the tangent line at P by averaging the
slopes of two secant lines.
(c) Use a graph of the function to estimate the slope of the
tangent line at P. (This slope represents the rate at which the
water is flowing from the tank after 15 minutes.)
0
A cardiac monitor is used to measure the heart rate of a patient
after surgery. It compiles the number of heartbeats after t min-
tes. When the data in the table are graphed, the slope of the
angent line represents the heart rate in beats per minute.
01
t
1909
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amos 94 CHAPTER 2 LIMITS AND DERIVATIVES 2.1 Exercises 1. A tank holds 1000 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 gallons) after t minutes. t (min) 5 10 15 25 20 30 V (gal) 694 28 0 444 250 111 (a) If P is the point (15, 230) on the graph of V, find the slopes of the secant lines PQ when Q is the point on the graph with t 5, 10, 20 25, and 30. sdi b 01 (b) Estimate the slope of the tangent line at P by averaging the slopes of two secant lines. (c) Use a graph of the function to estimate the slope of the tangent line at P. (This slope represents the rate at which the water is flowing from the tank after 15 minutes.) 0 A cardiac monitor is used to measure the heart rate of a patient after surgery. It compiles the number of heartbeats after t min- tes. When the data in the table are graphed, the slope of the angent line represents the heart rate in beats per minute. 01 t 1909

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Expert Answer

Step 1

Given,

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Let Vbe the volume of the water remaining in the tank (in gallons) after tminutes, Pbe the point (15, 250) on the graph of V. From the given table, set the point Qas a pair of (t, V (t)) That is, the ordered pairs are (5,694), (10, 444), (20, 111), (25, 28) and (30, 0)

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Step 2

Find the slope of the secant lines PQ when Q is the point on the graph with t = 5, 10, 20, 25 and 30.

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The slope of the secant lines between the points, P(15, 250) and (t, V (t)) is 250-V) where t={5,10,20, 25,30} (1) тРо 7 15 t Obtain the slope of the secant line between the points P(15, 250) and Q(5,694) Substitute 5 for tin equation (1). 250-V(5) тPо 15-(5) 250-694 10 -444 10 - -44.4 Thus, the slope of the secant line between the points P(15, 250) and Q (5,694) is -44.4 gal/min

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Step 3

Now, obtain the other slopes by substituting Q (10, ...

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5 10 20 25 30 Slope (mрo) | —44.4| -38.8| —27.8| —22.2| —16.6

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