multistep equations w/ variables on both sides
what is the first step in the equation
-2x+9-4=-4x-31+9
combine like terms (9-4) and (-31+9)
what does the A stand for in the equation
f(x)=a(1+r)^x
initial amount/starting value
what does r stand for in the equation
f(x)=a(1-r)^x
decay rate
simplify 4^3*4^5
4^8 or 65,536
solve -3x-7<2
-3x-7<2
-3x-7+7<2+7
-3x<9
-3/-3<9/-3
X>-3
solve
-2x+9-4=-4x-31+9
-2x+5=-4x-22
-2x+4x+5=-4x+4x-22
2x+5=-22
2x+5-5=-22-5
2x=-27
2/2=-27/2
X=-13.5
What does your rate of change or percentage rate have to be for your equation to show growth
more than 1/more than 100%
what does your rate of change or percentage rate have to be for your equation to show decay
less than 1/less than 100%
simplify (3^3)^4
3^12 or 531441
solve -6x-4<2(x-10)
-6x-4<2x-20
-6x+6x-4<2x+6x-20
-4<8x-20
-4+20<8x-20+20
16<8x
16/8<8x/8
2<x
solve
-3/2(x-4)=-4x+2
-3/2x+6=-4x+2
-3/2x+4x+6=-4x+4x+2
2.5x+6=2
2.5x+6-6=2-6
2.5x=-4
2.5/2.5=-4/2.5
X=-1.6
You deposit $750 in an account that pays 5% annual interest compounded yearly. Use the exponential growth formula y=a(1+r)^t to find your account balance after 8years. Round to nearest penny.
750(1.05)^8
$1108.09
a new car cost 23,000 and the value decreases by 15% each year. What is the value of the car after 8 years. y=a(1-r)^t
a=23000
r=.15
t=8
y=23000(1-.15)^8
y=23000(.85)^8
simplify (-3x^3y^2)^2
-3^2x^6y^5
9x^6y^4
3/2(x-4)>1/2x+6-5
3/2x-6>1/2x+1
3/2x-6-1>1/2x+1-1
3/2x-7>1/2x
3/2x- 3/2-7>1/2x-3/2
-7>-1x
-7/-1>-1x/-1
7<x
solve
-3x-4(4x-8)=3(-8x-1)
-3x-16x+32=-24x-3
-19x+32=-24x-3
-19x+24x+32=-24x+24x-3x
5x+32=-3
5x+32-32=-3-32
5x=-35
5x/5=-35/5
X=7
In 2000 Flordia's population was at 16million. Since 2000, the states population has grown 2% each year. Whats Flordias population in 2006?
y=16,000,000(1+0.2)^6
y=16,000,000(1.02)^6
y=18,018,598.71
18,018,598 peopleThe population of a town is decreasing at a rate of 3% per year. In 2000 there were 1700 people. Write an exponential decay function to model the situation. Then find the population in 2011.
a=1700 r=3%-0.03 y=a(1-r)^t
y=1700(1-0.03)^t
y=1700(0.97)^t
Y=1700(.97)^11
Y=1216.01238525
1,216 people
13-4^3/18-4^2+1
-17
solve -4<-3x-13<26
9<-3x<39
9/-3<x<39/-3
-3>x>-13
solve
2/5x-15=5/8x-16
2/5x-15=5/8x-16
2/5x-15+15=5/8x-16+15
2/5x=5/8x-1
2/5x-5/8x=5/8x-5/8x-1
X(2/5-5/8)=-1
X(2*8/5*8-5*5/8*5)=-1(find common denominator)
X(16/40-25/40)=-1
X(-9/40)=-1
X(-9/40)(-40/9)=-1(-40/9)
X=5 5/9
part A since 1995 the daily cost of patient care in the U.S. has increased by 4%. The average for such cost in 1995 was $968 dollars per day. Write an equation to model the cost of hospital care since 1995.
part B Use your equation to estimate the approximate cost per day in 2010. round to the nearest penny.
part A a=965 r=4%-0.04 y=a(1+r)^t
y=968(1+0.04)^t
y=968(1.04)^t
part B y=968(1.04)^t
t=2010-1995=15
y=968(1.04)^15
y=1745.313313
$1,743.31per day in 2010
A cup of coffee contains 130 milligrams of caffeine. If caffeine is eliminated from the body at a rate of 11% per hour, how long will it take for half of this caffeine to be eliminated from a persons body?
y=a(1-r)^t y=65 a=130 r=.11
65=130(1-0.11)^t
65/130=130/139(.89)^t
1/2=(.89)^t
log.89 1/2=log.89 (.89)^t
t~6hours
simplify (4x^2y)^2 * (-2y^2)^3
16x^4y^2 * -8y^6
-128x^4y^8
solve |10-4x|<2
|10-4x|<2
10-4x<-2 10-4x<2
10-10-4x<-2-10 10-10-4x<2-10
-4x<-12 -4x<-8
-4/-4<-12/-4 -4/-4<-8/4
x>3 x>-2
-3 and 2