5. For 0 ≤t≤ 6 seconds, a screen saver on a computer screen shows two circles that start as dots and expand outward. (a) At the instant that the first circle has a radius of 9 centimeters, the radius is increasing at a rate of 3 centimeters per second. Find the rate at which the area of the circle is changing at that instant. Indicate 2 units of measure.
5. For 0 ≤t≤ 6 seconds, a screen saver on a computer screen shows two circles that start as dots and expand outward. (a) At the instant that the first circle has a radius of 9 centimeters, the radius is increasing at a rate of 3 centimeters per second. Find the rate at which the area of the circle is changing at that instant. Indicate 2 units of measure.
Chapter3: Polynomial Functions
Section3.5: Mathematical Modeling And Variation
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Transcribed Image Text:6. For 0 ≤ t ≤ 6 seconds, a screen saver on a computer screen shows two circles that start as dots and expand
outward.
(a) At the instant that the first circle has a radius of 9 centimeters, the radius is increasing at a rate of
3
centimeters per second. Find the rate at which the area of the circle is changing at that instant. Indicate
2
units of measure.
(b) The radius of the first circle is modeled by w(1)
for 0 ≤ ≤ 6, where w(r) is measured
in centimeters and t is measured in seconds. At what time t is the radius of the circle increasing at a rate
of 3 centimeters per second?
-0.5t
= 12 12e
Do not write beyond this border.
Transcribed Image Text:(c) A model for the radius of the second circle is given by the function f for 0 ≤ 1 ≤ 6, where f(t) is
measured in centimeters and t is measured in seconds. The rate of change of the radius of the second
circle is given by f'(t) = 1² – 4t + 4, Based on this model, by how many centimeters does the radius of
the second circle increase from time t = 0 to 1 = 3 ?
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