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ID: 2256182 • Letter: S
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Secure https//www.mathal om Student PlayerHomework aspx?homeworkId-46 1476656&question;!d 10&flushed; false&cld; 4802309¢eninyes; 2018 Spring Math 1324-29 Online Homework: 3.1 Score: 0 of 1 pt Gen Interest 3.1.75 LaQusha McKinley | 1/29/18 12:10 AM Save 10of10 (9 complete) HW Score: 66%, 6 6 of 10 pts Question Help * 0 34x2 + 3701x + 5808 T A low pro ction scenario fo the population of Smalt n USA r 1995 and 21 years after 1990 and the population is measured in thousands of people. is given by the fun t on y· where x is the ber of a. Find the input and output at the vertex of the graph of this model b. Interpret the values from part a c. For what years after 1995 does this model predict that the population will Iincrease? a. The | | at the vertex is xmT] and| (Round to the nearest hundredth as needed ) |atthe vertex is ys Enter your answer in the edit flelds and then click Check Answer parts Clear Al heck AnsExplanation / Answer
(a)
y = -0.34x2 + 37.01 x + 5808.8
So vertex of graph => dy/dx = 0 => -2*0.34 x + 37.01 = 0 => 0.68 *x = 37.01 => x = 37.01/0.68 = 54.42
y(54.42) = -0.34*(54.42)2+37.01*54.42+5808.8 = 6816
Therefore input is x = 54.42 and output is y = 6816
(b)
This value is the maximum value of output for all input ie population is maximum at x = 54.42 years
ie year is = 1990+54.42 = 2044.42 .
(c)
The population will increase till 2044.42 , ie 2044.42 - 1995 = 49.42 years from 1995
Given S = 8+64t -16t2 = 68 we have to find t
Now , 8+64t -16t2 = 68
=> 16t2-64t+68-8 = 0
=> 16t2-64t+60 = 0
=> 4t2-16t+15 = 0
=> 4(t2-4t+4) - 1 = 0
=> (t-2)2 = 1/4 = (1/2)2
=> t = 2-1/2 , 2+1/2
=> t = 3/2 seconds, 5/2 seconds.
Two times means one time is during when ball is going up and one time is when ball is coming down after reaching maximum height
Therefore ball reaches height of 68 m at t= 3/2 = 1.5 seconds after throwing upwards.
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