Ma1210 Mod3 Essay

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MA1210 Mod3 3.1 Quadratic and Exponential Functions 1. Jerry wants to purchase some items whose cost function is C=3x+5, where x is the number of items. If Jerry spends between $50 and $80, find the minimum and maximum number of items that he can purchase. C=3x+5 X=(c-5)/3 answer: 15 items min X=(50-5)/3 x=15 25 items max X=(80-5)/3 x=25 2. A projectile follows a parabolic path whose height, in meters, is given by the function f(x) = -x2 + 2x +2. Find the maximum horizontal distance that the projectile may cover. 0 = -x2 + 2x + 2 Completing the square 0 = -(x2 - 2x ) +2 0 = -(x2 - 2x + 1) + 2 + 1 answer: x=2(1+V3) 0 = -(x - 1)2 + 3 -3 = -(x - 1)2 3 = (x - 1)2 ±√3 = x - 1 1 ± √3 = x 3. An archer’s arrow follows a parabolic path. The height of the arrow f(x) is given by f(x) = -16x2 + 200x +4, in feet. Find the maximum height of the arrow. f(x) =-16x+200x+4 answer: 629 feet a=-16 b=200 =-16 x 625/16 +50 x 25 + 4 = -625 + 1250 + 4 = 629 4. At a grocery store, the number of customers arriving per hour is shown by the function f(x) = 2x+1. Find the number of customers that arrived in the 6th hour. F(x)= 2x+1 X=6 answer=13 F(6) =2*(6) +1 =12+1=13 5. The profit of an organization is calculated by the function P(x) = x2– 4000x + 7800000, where x is the number of units sold. If the net profit is 3800000, find the number of items sold. P(x) =x^2 – 4000x + 7800000 3800000 = x^2 -4000x + 7800000 answer: number of items sold= 2000 X^2-4000x+4000000=0 (x-2000) ^2=0 X=2000 P(2000) =3800000 6. The value of a machine depreciates according to the function f(x)=20000(1/2)x , where x is the time in years from the purchase of the machine. Find its value after 3 years. 1(x)=200000(1/2)^x 20,000(.5)

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