Growth or Decay
y=4(2)x
Growth
Write an explicit arithmetic formula for the sequence: 3, 8, 13, 18, 23...
f(n)=3+5(n-1)
Describe the domain and range of this graph on the board.
D: all real numbers
R: y> -3
Write the following in exponential form: The cube root of the quantity x to the 7th power.
x7/3
Decay factor is 0.98, or it's retaining 98% of it's original value each year.
y=0.5(8)6x
Growth
Write an explicit formula for the geometry sequence: 60, 30, 15, 7.5
f(n) = 60(0.5)n-1
Describe the end behavior of the graph.
As x increases, y increases and
as x decreases, y approaches, but never reaches, -3
Write the following in simplest radical form: y raised to the 2 power, then raised to the three fourths power
The square root of y to the third power
Name the next term in the sequence: 58, 49, 40, 31, ...
22 (said in some creative way)
The value of a car depreciates 12% every year
Decay
Find the next 3 terms in the sequence: 1, 4, 9, 16...
25, 36, 49
If the graph is f(x), show what the graph of g(x) would look like, given: g(x) = f(x) + 4
Simplify without a calculator: 64 to the two-thirds power.
16
Write an equation to show the value of $1,000 invested in an account that gives 3% annual interest compounded semi-annually.
A = P(1+0.015)(2t), but say 2 differently!
If g(x)=2,500(1-0.04)x, what is the growth or decay factor (and is it growth or decay?)
0.96, decay
Write a recursive formula for the following sequence:6, 17, 28, 39...
f(1)= 6
f(n) = f(n-1) + 11
for n > or = to 2
Graph: f(x) = 4(0.5)x
Should show y-int: (0,4), decay and two other points
The cube root of the quantity 27 times x to the 6th power
3x2
Explain a possible meaning for this equation: A = 2,000(1+0.02)t
You had a couple of $1000 loans, each accruing interest at a rate that was half of 4%. :)
($2,000 growing at 2% each year)