Question

The population of a certain state (in thousands) from 1994 (t = 0) to 2004 (t = 10) is modeled by the polynomial p(t) = -0.27t² + 107t + 6082. a. Determine the average growth rate from 1994 to 2004. b. What was the growth rate for this state in 1996 (t = 2) and 2004 (t = 10)? c. Use a graphing utility to graph p' for 0 ? t ? 10. What does this graph tell you about population growth in this state during the period of time from 1994 to 2004? a. The average growth rate from 1994 to 2004 is thousand people / year. (Type an integer or a decimal.) 

          The population of a certain state (in thousands) from 1994 (t = 0) to 2004 (t = 10) is modeled by the polynomial
p(t) = -0.27t² + 107t + 6082.
a. Determine the average growth rate from 1994 to 2004.
b. What was the growth rate for this state in 1996 (t = 2) and 2004 (t = 10)?
c. Use a graphing utility to graph p' for 0 ? t ? 10. What does this graph tell you about population growth in
this state during the period of time from 1994 to 2004?
a. The average growth rate from 1994 to 2004 is thousand people / year.
(Type an integer or a decimal.)
Show more…
The population of a certain state (in thousands) from 1994 (t = 0) to 2004 (t = 10) is modeled by the polynomial p(t) = -0.27t² + 107t + 6082. a. Determine the average growth rate from 1994 to 2004. b. What was the growth rate for this state in 1996 (t = 2) and 2004 (t = 10)? c. Use a graphing utility to graph p' for 0 ? t ? 10. What does this graph tell you about population growth in this state during the period of time from 1994 to 2004? a. The average growth rate from 1994 to 2004 is thousand people / year. (Type an integer or a decimal.)

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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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Transcript

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00:01 The function p of t equals negative 0 .27t squared plus 107t plus 6 ,082 models the population of a certain state in thousands from 1994 where t equals 0 to 2004 where t equals 10.
00:12 Find the average growth rate from 1994 to 2004.
00:16 So that would just be p of 10 for 2004 minus p of 0 for 1994 divided by 10 minus 10 minus 0 for 1994 divided by 10 minus 0.
00:32 So we need to plug 10 into that function.
00:35 So that would be negative 0 .27 times 10 squared plus 107 times 10 and then plus 6 ,082.
00:53 They give us 7 ,125 and then plugging in p of 0 is easy.
00:59 This would just be 0, this would be 0 and that would just be minus 6 ,000.
01:03 And then 10 minus 0 is 10.
01:06 So we have that 7 ,125 we would minus 6 ,882 and then that gives us 1 ,03 divided by 10.
01:21 So it's about 104 .3 and that would be 1 ,04 .3 and that would be 1 ,000 people per year is what that represents.
01:39 Next we want to find the growth rate in this state in 1996 where t equals 2 and in 2004 t equals 10.
01:46 We're going to need the derivative of this function to do that.
01:49 So p prime of t would be negative 0, negative 0 .27 times the derivative of t squared, which should just be 2t, plus the derivative of 107 t would be 107, plus the derivative of the constant would just be 0.
02:07 So we can simplify that to negative 0 .54t plus 107...
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