What is the general formula for the geometric sequence?
A(n) = a(r)^n-1; a = first term #, r = common ratio
100
Does the following equation represent exponential growth or decay? Why?
y=32(0.75)^x
Decay; 0<0.75<1, as x values increase, y values decrease
200
Simplify (a^6)(b^3)(a^2)b^-2)
a^8(b)
200
Simplify (4x^3)^2
16x^6
200
(c^2d^-3)/(c^3d^-1)
1/(cd^2)
200
Find the common ratio. Then find the next three terms in the sequence: -0.2, -0.4, -0.8, -1.6,...
common ratio = 2; -3.2, -6.4, -12.8
200
For which function(s) will values of y decrease as values of x increase?
a. y = 12.5(1.325)^x
b. y = 5000(0.98)^x
c. y = 300(0.06)^x
d. y = 1.02^x
b and c because the growth factor is between 0 and 1.
300
(x^5y^2)(x^-6y)
y^3/x
300
Simplify (13g^4)^-1
1/(13g^4)
300
(m^-2)/(m^-5)
m^3
300
Find the first, fifth, and tenth terms of the sequence that has the rule A(n) = -3(2)^n-1
-3, -48, -1536
300
Suppose $24 had been invested in 1626 in an account paying 4.5% interest compounded annually. What will the balance be in 2000?
You can round to the nearest million.
$339,000,000
400
Evaluate the expression for a = 3, b= 2, and c= -4.
(c^-a)b^(ab)
-1
400
(2xy)^3(x^2)
8x^5y^3
400
Simplify (a^3b^2c^-4)/(a^-2b^5c^-9)
(a^5c^5)/(b^3)
400
You drop a handball from a height of 1 meter. Each curved path has 64% of the height of the previous path.
Write a rule for the sequence using centimeters. The initial height is when n = 1.
A(n) = 100(0.64)^n-1
400
Write an exponential function to represent a $24,000 that decreases in value 3.5% each year.
y = 24,000(0.965)^x
500
Evaluate the expression for a = 3, b= 2.
a^-b(b)
2/9
500
Simplify (4xy^3)^2(x^3)^-3
(16y^6)/x^7
500
Simplify (3^2 * 5^0)/(2^3)
9/8
500
How can you determine whether a sequence is arithmetic or geometric?
If all consecutive terms has a common difference, the sequence is arithmetic. If all consecutive terms have a common ratio, the sequence is geometric.
500
A population of 24,500 people has been increasing at a rate of 1.8% a year. What will be the population in 15 years if it continues at that rate?