2.1-2.2
Find an equation that gives the nth term of each sequence, Use the initial value (k=0) of the sequence in your equation.
(8, 16, 32, 64,……..)
gn= 4 x 2n-0
Is the exponential a growth of a decay?
2(0.3)x
It’s a DECAY because a > 0 and 0 < b < 1
Let f(x)=3x
g(x)= 8 x 4x
Name the Transformation.
Vertical stretch of 8, left 2
The value V of a outdoor pool is purchaced for $1,800 and decreases by 12% every year t.
Write the function to model this scenerio.
V(t)=1,800(0.85)t
PREDICTED-ACTUAL=?
ERROR
What is the 63rd term?
(56, 45, 34, 23,………….)
a63 = -626
f(x)= -2(8)x
Is it Increasing/decreasing?
is it concave up/down?
What is the end behavior?
The function is…..
decreasing
concave down
End Behavor:
Let h(x)= 2 x 7(X/2)
Find h(1)
h(1)=2 x square root of 7
The table shows how much debt Marie accumulates every year with interest being applied.
Year(t): 1 2 3 4 5
Debt(y): 16 19 40 67 153
How much will Marie owe Josh in 8 years?
Marie will owe Josh $747.08 in 8 years.
Describe what a good residual graph looks like.
The points have no clear pattern.
It is known that f(x) is a linear function and that it passes through the points (6,2) and (1,4). Write an equation for this function.
2 + 2/6 (x-6)
The values are output values of an exponential function of the form f(x) = a x bx. Write the function and input values that represent the output value.
8 x 8 x 8 x 8 x 1.6
f(x) = 1.6(8)x
where x=4
Let f(x) = 3x
g(x)= f(x)/12
Name the Transformation.
Vertical Compression of 1/12, Right 2
There is a fossil that is 200 years y old. It’s half-life is 6,200 years t.
Write a function to model this scenario.
y(t)=200(0.5)t/6,200
The table below represents the amount of grey hair (h) Mrs. Hudson gets through her teaching years (y). FIND THE LINEAR REGRESSION CURVE.
Years Mrs. Hudson taught (y): 1 2 3 4 5
Amount of grey hair (h): 0 2 9 7 23
Y = 5.1x - 7.1
The following function is either linear or exponential. Identify the constant (slope or ratio) that causes the output values to change.
y=7 x 5x
Ratio of 2
f(x) = 7 (0.2)x
Is the function increasing or decreasing?
Is the function concave up or concave down?
What is the end behavior?
The function is….
Decreasing
Concave up
End behavior:
lim f(x) when x—negative infinity=infinity
lim f(x) when x—infinity = 0
Let f(x)=2x
g(x)= 4x
Horizontal Compression of 1/2
If f(d)=6d indicated the quantity increases by a factor of 6 every day, then what does f(t)=(64)(d/7) indicate?
The quantity increases by 64 a week.
FIND THE ERROR AT y = 24
IS IT AN OVERESTIMATE?
Years alive (y): 18 20 22 24 26
Pencils broken (p): 8 15 26 31 55
Y = 24 has an ERROR of 7
This is an overestimate
The following function is either linear or exponential. Which is it? Justify.
x: 5 12 19
f(x) 9 6 3
The function is LINEAR because as the input changes by 7, f has a constant rate of change of -3.
f(x)= -3(9)x
Is the function decreasing or increasing?
Is the function concave up or down?
What is the end behavior?
The function is…..
Decreasing
Concave Down
End Behavior:
lim f(x) when x—negative infinity=0
lim f(x) when x—infinity=negative infinity
Let f(x)=4x
g(x)= (f(x))-4
Name the Transformation
Horizontal Compression of 1/4, reflect over y-axis
The table shows how much debt Marie accumulates every year with interest being applied.
Year(t): 1 2 3 4 5
Debt(y): 16 19 40 67 153
Use an exponential regression y=abx to model this data.
y = 7.355(1.781)x
Multiple submarines were tested to see how low the new model could go. A regression model was calculated with the pressure applied to the submarine (in pascal Pa) as input values and the depth it’s submerged (in feet) as the output values. A plot has a point labeled P at the coordinate (20,000, 52). What does point P indicate in this context?
The submarine that had 20,000Pa of pressure applied to it made it 52ft farther down than predicted.