Tables or Points
Growth or Decay
All about Functions
Extra Problems
100
What model does this table represent? Linear or exponential?
Can you build the equation with what is given?
Linear, subtracting 1.
No, we are missing the initial term
Bonus points for the group that can give me the equation.
100
What do you need for exponential growth?
What do you need for exponential decay?
y = a \cdot b^x
For growth, b must be more than 1
For decay, b must be less than 1
100
Determine the slope and y-intercept from the following equation:
y = -2x -5
Slope=-2
Y-intercept= (0,-5)
100
Evaluate the function
f(x)=20-4x for when x=(-2)
28
200
Linear or Exponential?
Exponential, multiply by 2
200
What is the secret phrase for this Rebus Puzzle?
Trail Mix
200
Identify the y-intercept (initial value) and the percentage of growth in the function f(x)=13(1.27)x
Initial Value: 13
Growth Rate: 27%
200
Match the function with its graph.
y = 2 \cdot (1/4)^x
It should be the Green Graph
300
Linear or Exponential?
Exponential, multiply by 1/4
300
Is the following function growth or decay? What's the percent of growth or decay?
y=15(1.15)x
Growth; 15%
300
A town of 3200, grows at a rate of 25 people every year. Find the equation for this situation.
y = 25x + 3200
300
Is there enough information to say if these points are a part of a linear or exponential graph?
{(0,4), (1,8)}
No, for two points, we NEED TO KNOW the pattern. Bonus points for anyone who can build both types of equations (linear and exponential).
400
Linear, Exponential, or neither? Why?
{(2, 4), (3, 6), (4, 8), (5,11)}
Neither. Last term does not follow the pattern.
400
Growth or decay? Percent of Growth or Decay?
y= 234(.93)x
Exponential decay. 7%
400
A scientist is testing bacteria starvation rates. Let's say they found the function to be represented as f(x)=1200(.85)x where 'x' is the number of hours passed. Find the number of bacteria after 6 hours [find f(6)]
452.58 bacteria
400
Give the rate of decay:
y = 35(0.65)x
r=.35
500
From the given coordinate points, is the function linear, exponential, or neither? What is the formula for this set of points?
{(1, -1), (2, 6), (3, -36)}
Exponential, multiply by -6
y = 1/6 \cdot (-6)^x
500
Sally invests $750 dollars into a bank that pays 7% interest.
What is the multiplier for the equation?
How much money will Sally have after 10 years?
1.07 or 107%.
Amount: $1475.36
500
Congratulations! You've found two Bags of Holding.
Bag #1 will take $25 in the beginning, but it will double the amount inside the bag every month.
Bag #2 will take $500 in the beginning, but it will add an extra $100 out of nowhere every month.
Which option is the better bag after 3? Why? At what point would one bag overtake the other?
Bag #2 would have $800 versus Bag #1 and $200.
At 6 months, Bag #1 would be better ($1600 > $1100)
500
The price of a car that was bought for $10,000 and has depreciated 10% yearly. Find the price of the car 8 years later.
$4304.67