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) 6 3 answer:2,500

20,000 *.125=2,500

7. An object is thrown, and it follows a parabolic...