Change in Arithmetic & Geometric Sequences
What is the general rule for the arithmetic sequence 1, 5, 9, 13, 17, . . .
an = 4n - 3
Given the explicit formula for the sequence
f(n) = 9 - 3(n - 4)
Write the first 10 terms of the sequence
{18, 15, 12, 9, 6, 3, 0, -3, -6, -9}
Compute the value of the function
f(x) = 6(3)x+1 for x = 2
f(2) = 162
Find f(x) = 3x when x = -2
3-2 = 1/9
Determine if the function represents exponential growth or exponential decay; find the y-intercept
y = 158(1.34)x
growth
y-intercept (0, 158)
What are the first four terms of the sequence
an + 5 + (-1)n
4, 6, 4, 6
Using the sequence, find the difference d and write the explicit rule, an
a0 = -7; a1 = -5, a2 = -3, a3 = -1, a4 = 1, a5 = 3, a6 = 5
d = 2
an = -5 + 2(n-1)
f(x) = -5(8)x for x = 1/3
f(1/3) = -10
Find g(x) = 3x+2 when x = -2
3-2+2 = 1
Write the exponential function that models the scenario
A new sports car sells for $65,000. It depreciates 22% every year. What is the value of the car after 4 years?
a= 65,000
b = 1 - 0.22
b = 0. 78
y = 65000(0.78)x
y = 65000(0.78)4
y = 24059.79
If a sequence has an explicit formula an = 12n +3; what is the a12?
a12 = 147
Given the arithmetic sequence where a1 = 17 and a8 = -39, state the domain and range of the sequence
d = -8
domain {1, 2, 3, 4, 5, 6, 7, 8}
range {17, 9, 1, -7, -15, -23, -31, -39}
Find an equation y = g(x) that describes the function characteristics
1. The value of g at x = 0 is 3
2. The output value of g doubles at every 1-unit increase in the input value
a = 3
b = 2
y = 3(2)x
Rewrite the function of g(x) = 3x + 2 in the form of h(x) =abx
g(x) = 3x+2
=3x(32)
=3x(9)
h(x) = 9(3)x
You have $15000 to invest in a retirement account. The fund increases at a rate of 10.8% per year. What will be the value of the investment at the end of 30 years?
a = 15000
b = 1 + .108
b = 1.108
y = 15000(1.108)x
y = 15000(1.108)30
y = 325,300.01
Using the formula: an = a1*rn-1 find a6 of the geometric sequence: 3, -15, 75, ...
a6 = -9375
Complete the sequence
a1 = 64, a2 = 32, a3 =? a4 =?, a5 = 4, a6 =? a7 = ?
a3 =16 a4 =8, a6 =2 a7 =1
Determine the formula for the function from the given values
x: -2, -1, 0, 1, 2
f(x): 3/4 3/2 3 6 12
ratio: 2
f(x) = 3(2)x
What is the transformation of the graph f(x) = 4x
g(x) = f(x - 3)
g(x) = 4x-3
A population count of 1246 black bears were found in a region of North Carolina. The population has been increasing at a rate of 2.25% per year. If tis growth rate continues, how many bears will populate the region in 5 years?
a = 1246
b = 1 + 0.0225
b = 1.0225
p(t) = 1246(1.0225)t
p(t) = 1246(1.0225)5p(5) = 1392 bears
What is the common ration of the sequence AND put it in explicit form
3, -9, 27, -81, ...
r = -3
an = 3(-3)n-1
Write the first four terms of the sequence
an = 3n - 4
a1 = -1
a2 = 2
a3 = 5
a4 = 8
Determine the formula for the function for the given values
X: -2, -1, 0, 1, 2
g(x): 20 10 5 5/2 5/4
ratio: 1/2
g(x) = 5(1/2)x
Explain the transformation for the graph
g(x) = 4x-3
Shift 3 units right
Use the formula for compound interest to answer the scenario
A(t) = P( 1 + r/n)nt
You have invested $3000 in a mutual fund paying 7.25% interest compounded quarterly, how much will be in your account after 5 years?
P = 3000
r = 0.0725
n = 4
t = 5
A(t) = 3000(1 + 0.0725/4)4t
A(5) = 3000(1.018125)4(5)
A(5) = 4296.78