P.o.D. – Solve each equation for the indicated variable.
1.) P=2L+2W for W
2.) A=L(W) for L
3.) C=2πr, for r
4.) A=12h(B+b), for b
5.) A=πr2, for r
1.) W=P-2L2
2.) L=A/W
3.) r=C2π
4.) b=2Ah-B
5.) r=Aπ
1-8: Explicit Formulas for Sequences
Learning Target(s): I can find terms of sequences; use a graphing utility to graph functions and generate tables for functions.
Sequence – an ordered list of numbers
Term of a Sequence – each item in the sequence
Explicit Formulas:
EX: Consider the formula tn=3n-4.
a.) Assuming n1, what are the first 4 numbers in the sequence defined by the formula?
t1=31-4=3-4=-1
t2=32-4=9-4=5
t3=33-4=27-4=23
t4=34-4=81-4=77
b.) Evaluate t10 and explain what it means.
t10=310-4=59,045
This means that the 10th term in the sequence is 59,045.
Compound Interest:
A=P(1+rn)nt, where r is the rate, p is the principal, n is the number of times compounded per year, and t is the number of years invested.
EX: Alfonso has invested $750 for 1 year at 8% annual interest.
a.) If the interest is compounded semiannually, how much will he have at the end of 1 year?
A=750(1+.082)(21)=
750(1.04)2=
$811.20
b.) How much money will Alfonso have at the end of the second and third years?
A2=750(1+.082)22=$877.40
A3=750(1+.082)23=$948.99
c.) How much money will he have after 10 years?
A10=750(1+.082)210=$1643.34
EX: Ashley put $750 in a bank account that pays 4.2% interest at the end of each year. During the nth year, the account balance is given by An=750(1.042)n-1.
a.) Complete the table below.
Year / 1 / 2 / 3 / 4 / 5Balance
750 / 781.50 / 814.32 / 848.52 / 884.16
b.) In which year will the balance in the account first pass $1000?
Year 8
Upon completion of this lesson, you should be able to:
1. Identify a sequence
2. Find the numbers in a sequence
3. Compute compound interest
For more information, visit https://www.khanacademy.org/economics-finance-domain/core-finance/interest-tutorial/compound-interest-tutorial/v/introduction-to-compound-interest
Hw Pg.57 2-8, 10-20
Quiz 1.5-1.8 tommorrow