Algebra 1--Unit 4

Growth or Decay

100

y=4(2)^x

Growth

200

y=0.5(8)6^x

Growth

300

The value of a car depreciates 12% every year

Decay

400

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

Sequences

100

Write an explicit arithmetic formula for the sequence: 3, 8, 13, 18, 23...

f(n)=3+5(n-1)

200

Write an explicit formula for the geometry sequence: 60, 30, 15, 7.5

f(n) = 60(0.5)^n-1

300

Find the next 3 terms in the sequence: 1, 4, 9, 16...

25, 36, 49

400

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

Graphs

100

Describe the domain and range of this graph on the board.

D: all real numbers

R: y> -3

200

Describe the end behavior of the graph.

As x increases, y increases and

as x decreases, y approaches, but never reaches, -3

300

If the graph is f(x), show what the graph of g(x) would look like, given: g(x) = f(x) + 4

Shift f(x) up 4 units. New y-int is (0,2), new asymptote is y = 1.

400

Graph: f(x) = 4(0.5)^x

Should show y-int: (0,4), decay and two other points

Rational Exponents!

100

Write the following in exponential form: The cube root of the quantity x to the 7th power.

x^7/3

200

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

300

Simplify without a calculator: 64 to the two-thirds power.

16

400

The cube root of the quantity 27 times x to the 6th power

3x²

Don't say 2

100

Describe the exponential decay shown in this equation: f(x) = 400(1-0.2)^t

Decay factor is 0.98, or it's retaining 98% of it's original value each year.

200

Name the next term in the sequence: 58, 49, 40, 31, ...

22 (said in some creative way)

300

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! 

400

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)