LG 10:Modeling with quadratics and exponentials

answers to quadratic equations

100

(3±√63)/9 

(1±√7)/3

200

Use your calculator to identify the solutions and vertex of the quadratic (round to nearest tenths place): 

-3x2-14x+23

x=1.3, x=-5.9 (-2.3, 39.4)

300

use the quadratic formula to find the solutions to to function (round to nearest tenths place): 

-4x²-16x+34

x=5.5, x=-1.5

quadratic word problems with height

100

The equation for the object's height (h) at time (t) seconds after launch is h(t) = –4t² + 12t + 40. When does the object strike the ground?

t=5

200

The equation for the object's height (h) at time (t) seconds after launch is h(t) = –2t² + 6t + 36. When does the object strike the ground and what is its maximum height?

t=6, max height: 40.5

300

The equation for the object's height (h) at time (t) seconds after launch is h(t) = –6t² + 18t + 60. When does the object strike the ground and what time is it at its maximum height?

t=5, maximum height when t=1.5

exponential growth vs. decay

100

does the function show decay or growth and what is the rate of change in percent form? 

y=4(0.5)^x

decay of 50%

200

does the function show decay or growth and what is the rate of change in percent form? 

y=3(0.8)^x

decay of 20%

300

does the function show decay or growth and what is the rate of change in percent form? 

y=7(1.25)^x

growth of 125%

exponential word problems

100

since january of 2000, the population of Exponentialville has grown at a yearly rate of 3.1% according to the model y=50,000(1.031)^x, where x is the number of years since january of 2000. What will the population be in 2005 if the growth continues at the same rate?

58245 

200

since 2000, the population of Exponentialville has grown at a yearly rate of 2.3% according to the model y=34,000(1.023)^x, where x is the number of years since 2000. Use the model to predict the nu the number of years until the population of Exponentialville will first reach 1,000,000. 

x=148.7

300

an energy drink contains 150 milligrams of caffeine. the caffiene is eliminated from the body at a rate of 10% per hour. how long will it take for 75% of the caffeine to be eliminated? 

13.03 hours

maximizing vs. minimizing area

100

using the variables x (width), L (length), and y (area) make the equation for area and perimeter. 

area: y=xL

perimeter: 2x+2L

200

a gardener wants to make a rectangular plot of land for her potatoes, but she needs to make a fence for it so her dog doesn't dig up the potatoes! she has 30 ft of fencing and wants to make the biggest area possible. what is the biggest area she can have?

56.25ft 

300

a gardener wants to make a rectangular plot of land for her potatoes, but she needs to make a fence for it so her dog doesn't dig up the potatoes! she has 30 ft of fencing and wants to make the biggest area possible. find the value of x and L when the area is the largest possible.  

x=7.5, L=7.5