Determine whether each table below represents a linear function.
-
Upload
ami-taylor -
Category
Documents
-
view
230 -
download
0
Transcript of Determine whether each table below represents a linear function.
a) Use the tables above to make predictions. Will there be enough grain to feed the world in 2020? In 2030?
b) What kind of factors could change your predictions?
You-Try (with partner)
Consecutive outputs are the outputs for consecutive inputs.
The differences between consecutive outputs are recorded in the Δ column.
If these differences are the same, that value is called the constant difference or common difference.◦ This also means the function is linear.
Definitions
In the table, variables a and b represent arbitrary numbers.
a) Copy and complete the table in terms of a and b.
b) Find a linear function that matches the table.
You-Try (with partner)
Input Output Δ0 b a1 a2 a3 a4 a5
Recursive rules tell how to get from one output to the next output.
An initial output, called the base case, must also be given.
Recursive Rules
Base Case:
Recursive Rule:
What are the first 10 numbers in the Fibonacci Sequence?
Fibonacci Sequence 11
00
F
F
21 nFnFnF
Does the recursive rule
define the function ?
Test your answer with an input of ½
You-Try (with partner)
0if51
0if3
nnf
nnf
xx 53
James saves $85 and wants to invest it. Investment L will add $5 at the end of every
year to James’s account. Investment E will add 5% of the current
amount at the end of every year.a) Which investment is better in the short
run?b) Which investment is better in the long
run?
You-Try (with partner)
Warm-Up: January 12, 2015 You may use a calculator (graphing or
otherwise) to complete this warm-up.
An exponential function is one where x is in the exponent.
The ratio of outputs is one output divided by the previous output.
Exponential functions have a constant ratio.
Definitions
Tony invests $600 in a savings account that earns 3% interest at the end of each year.
a) How much interest will he have earned after 1 year?
b) How much interest will he have earned after 2 years?
Warm-Up: January 13, 2015
Tony finds a new investment for his $600 that earns 6% interest at the end of each year.
a) How much interest will he earn after 2 years?
b) Is it double the amount he would earn with the 3% investment?
You-Try (with partner)
Most bank accounts calculate interest based on the current balance and add the amount to the account.
When the interest on the current balance includes interest on previous interest, it is called compound interest.
Compound interest is usually calculated and added to the account more often than once per year.
Interest
Tony finds another investment that offers 5.9% interest compounded monthly. Why is this the best option so far?
Example 1
A = current amount P = principal (the original investment) r = Interest rate (APR), expressed as a
decimal, not as a percent n = Number of times per year interest is
calculated t = Time, measured in years
Interest Formulatn
n
rPA
1
Tony decides to invest his money in a CD (certificate of deposit) that earns 6% APR, compounded annually. How many years will it take for his investment to double?
Example 2
On Monday we looked at functions of the form
a) For what values of b will the outputs be increasing (for increasing inputs)?
b) For what values of b will the outputs be decreasing (for increasing inputs)?
Warm-Up: January 14, 2015
xbaxf
Exponential growth occurs when a>0 and b>1.
Exponential decay occurs when a>0 and 0<b<1.
Exponential Growth and Decay xbaxf
Real World Applications
Exponential Growth Exponential Decay
Population growth◦ People◦ Bacteria
Continuous compounding of interest
Nuclear reactions Processing power of
computers (Moore’s Law)
Half-lives of radioactive isotopes◦ Carbon dating◦ Other dating to determine
ages of dinosaurs, etc. Rate of cooling (temp.) First order chemical
reaction rates Atmospheric pressure
(as a function of height)
Read Section 5.17 (pages 462-464) Page 465 #5-8
◦ Graphs must be on graph paper
Page 467 #1-5
Assignments