Arithmetic Sequences
Write the explicit arithmetic sequence formula
an= a1+d(n-1)
Which is the 7th term of the sequence?
2, -10, 50, -250
31,250
What formula would you use to find the amount of money earned in a simple interest account?
f(x)=abx
Write the compounded interest formula
A= P(1+r/n)nt
What is the exponential formula?
f(x)=abx
Write the recursive formula
An=An-1+d
Find the 6th term of the geometric sequence for which A1= -7 and r=1/3
7/243
Tanner invests $106 into savings account that earns 1.5% interest every year. If he does not deposit or withdraw any money from the account, how much money will be in his account in 10 years?
106(1+.015)10
$123.01
In the compound interest formula, the variable "n" represents what value?
The number of times interest is compounded per year
In the exponential formula, what does each variable represent?
a= initial amount
b= rate
x= time
Write the explicit formula for the sequence
-9,-6,-3,0...
an=-9+(n-1)*3
Find the 4th term of the geometric sequence for which A1=-8 and r= -1/2
1
Orangutans are critically endangered species with a population of 105,000 that is expected to decrease by 12% each year. How many orangutans will there be in 8 years? Round to the nearest whole number
About 37,762
Krystal was given $3000 when she turned 2 years old. Her parents invested it at a 2% interest rate compounded annually. No deposits were made or withdrawals. Write the expression that can be used to determine how much money Krystal had in the account when she turned 18
3000(1+0.02)16
Barack Obama has put out the first pair of official presidential sneakers- the Barry Zeros. The value of a pair of Barry Zeros depreciates by 5% every year they are worn. If your new pair of Barry Zeros cost $300, how much will your pair be worth after 9 years of wearing them?
300(1-0.05)9
$189.07
Find the first four terms in the sequence
an=(2n-1)2
1,9,25,49
Find the 4th term of the geometric sequences for which A1= 7 and r=-1/5
-7/125
Weevils are slowly killing all the flowering plants in the garden. The number of plants left can be modeled by the function f(d)=86(0.74)d, where d is the number of days that have passed since the start of the Spring.
What is the percent change in plant population every day?
1-.74= .26
.26*100= 26
26%
Rhonda deposited $8000 in an account in the Merrick National Bank, earning 4.2% interest, compounded quarterly. She made no deposits or withdraws. Write an equation that can be used to find her account balance, B, after t years.
8000(1.0105)t
Is the following function growth or decay? Explain your answer
f(x)= 12000(.2)x
Decay because the exponential factor is less than 1
Write the recursive formula for the sequence
-3, -10, -17, -24...
an=an-1-7
Suppose you record the number of claps during a thunderstorm. The table below shows the pattern of claps over time. If the pattern continues, how many total claps will occur in 32 seconds?
Seconds Total Claps
1 2
2 3
3 4
8 5
7 claps
The population of Racine, Wisconsin, has grown by 2.3% every year since January 1992, when the town had 63,450 residents. How many new residents arrived between 1998 and 2001?
63450(1+0.023)x
1998: 63450(1+0.023)6 = 72725
2001: 63450(1+0.023)9 =77860
77860-72725=5135
5134 or 5135
A student invests $500 for 3 years in a savings account that earns 4% interest per year,compounded monthly. No further deposits or withdraws are made during this time. What is the balance in the account at the end of 3 years?
Round to the nearest hundredths place
500(1+.04/12)12*3
563.64
Create a scenario that represents exponential growth. Write the function for your scenario
Answers will vary