Properties of Exponents
Radical & Rational Exponents
Exponential Growth & Decay
Solving Exponential Equations
Geometric Sequences
100
Simplify:
(3^2)/3^-5
3^7
100
Convert to rational exponent:
root3(49^4)
49^(4/3)
100
What value tells you if it is growth or decay?
How do you know if it's a growth?
How do you know if it's a decay?
The "b" value tells growth or decay.
If b-value is greater than 1: growth.
If b-value is between 0 and 1: decay.
100
Solve:
8^(3x-4)=8^(2x+1)
x=5
100
What is the explicit rule formula?
an=a1(r)n-1
200
Simplify:
a^4*a^6*a^2
a^12
200
Simplify without a caluculator:
root5(32^3)
8
200
Does this functions represent exponential growth or decay? What's the percent growth/decay rate?
f(x)=7(1.07)^x
Exponential Growth
Rate: 7%
200
Solve for the variable:
4^x=2^(x-3)
x=-3
200
Write the explicit formula for this geometric sequence.
2,6,18,54, ...
2(3)^(n-1)
300
Simplify:
(2x^3y^2)^4
16x^12y^8
300
Simplify without a calculator:
256^(3/4)
64
300
What is the initial value of the following formula, and what is the growth/decay rate:
y=5(1.3)^x
The initial value is 5.
The growth rate is 30%
300
Solve:
(1/3)^(x-1)=27
x=-2
300
Write the explicit formula for this geometric sequence.
150,-120,96,-76.8, ...
150(-4/5)^(n-1)
400
Simplify (positive exponents only):
((2x^-2)/(5y^4))^-2
(25x^4y^8)/4
400
Simplify without a calculator:
343^(2/3)
49
400
What is the initial value of the following formula, and what is the growth/decay rate:
y=(0.01)^x
The initial value is 1.
The decay rate is 99%
400
Solve:
(1/27)^(4-x)=9^(2x-1)
x=-10
400
Does the following table represent a geometric sequence?
No, the x-values do not go up by the same amount
500
The human body produces about 4.8 × 106 red blood cells in 4 × 10−2 minute. How many red blood cells does the body produce each minute? Write your answer in scientific notation and in standard form.
1.2 × 108 red blood cells
120,000,000 red blood cells
500
The average tuition cost of a 4-year college increases from $20,125 to $25,900 over a period of 6 years. The average tuition cost of a 2-year college increases from $8540 to $10,950 over the same period. Which has a greater annual inflation rate? Explain
Use formula: r=(F/P)^(1/n)-1
4-year college
4-year: 4.3%
2-year: 4.2%
500
Larry invested $27,000 in a savings account that pays an annual interest rate of 1.8%. The savings account is set to compound quarterly. How much is in Larry’s account after 5 years?
$29,536.74
500
The function f(x)=2300(0.995)^x models enrollment in a high school, where x is the number of years after 2005. What will the enrollment be in 2010?
2243
500
What would the starting value be for the following geometric sequence?
___ , 120, 300, ...
48