Algebra Test IV

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A colony of bacteria starts with 300 organisms and doubles every week. How many bacteria will there be at 8 weeks?
300(2)^8=76800
A population of fruit flies triples every month. How many fruit flies will there be after 6 months is originally there were 24 flies?
How many months will go before there are 30000 flies?
24(3)^6=17496
Y1=24(3)^x
Y2=30000
=(6.49,30000)
In 1998, the average annual cost of a public college was $10069 and costs were climbing by 6% per year. Is the growth remain steady, how much would a year of college cost in 2004?
How much would it cost in 2020?
10069(1.06)^6=14283.06
10069(1.06)^22=36284.01
Iodine-131 is a radioactive element that decays at a rate of 8.3 % per day. How much of a 12 gram sample will be left after 1 week?
When will it be down to 1 gram?
y=12(.917)^7=6.54
Y1=12(.917)^x
Y2=1
=28.67
A rancher who started with 800 head of cattle finds that he's herd increases by a factor of 1.7 every 3 years. What is the yearly growth factor?
What is the yearly growth rate? How many will he have in 9 years?
800(1.7)^(1/3)
(1.7)^(1/3)=1.19
1.19-1=.19=19%
800(1.7)^(9/3)=3930.4
During a summer spraying program the mosquito population was reduced by 25% every 2 weeks. If the mosquito population was originally 200,000, how many mosquitos remained after 3 weeks?
What is the weekly decay factor? What is the weekly decay rate?
200000(.75)^(3/2)=129903.8
(.75)1/2=.866
.866-1=-13.4%
The number of bass in Hidden Lake has declined to half its previous level every 5 years since 1960, when it was estimated to be a 8000.
How many bass were in the lake in 1970?
How many were in the lake in 1987?
y=8000(1/2)^(10/5)=2000
y=8000(1/2)^(27/5)=189
A population of geese grew from 400 to 720 in 5 years. Is the population growth is linear, what was its annual rate of growth? If the population growth is exponential, what was its annual rate of growth?
(720-400)/(5-0)=320/5=64
y=400a^x
720=400a^5
(720/400)=(400/400)a^5
1.8=a^5
5^√1.8=5^√a^5
1.125=a
1.125-1=.125=12.5%
The world's tiger population declined from 10400 in 1980 to 6000 in 1998. If the population declined linearly, write an equation to describe the decline. If the population declined explicitly, write an equation to describe the decline.
(10400-6000)/(0-18)=-244.44 y=-244x+10069 (6000/10400)=a^18 18√.576923......=.9699 y=10400(.9699)^x
A culture grows continuously at a rate of 3.5% per day. If there were 200 in the population originally, right and exponential function that models the growth. How long will it take for the population to double in size?
y=200e^.035t
y=200e^.035(8)=265
400=200e^.035t
(400/200)=(200/200)e^.035t
ln2=lne^.035t
ln2=.035t
(ln2/.035)=19.8
A population is declining at a continuous rate of 3.5% per day. If there were 200 in the population originally, write an exponential function that models the decay. What will the population be in 8 days? How long will it take for the population to be 1/2 the size it was initially?
y=200e^-.035t
y=200e^-.035(8)=151
100=200e^-.035t
(100/200)=(200/200)e^-.035t
(1/2)=e^-.035t
ln(1/2)=-.035tlne
ln(1/2)/-.035=-.035t
=19.8 years
Sue has $400 invested in an account that pays 2.1% invest quarterly. If she leaves the money for 3 years, how much will she have? When will her investment double?
400(1+.021/4)^4t
What is the effective rate for money that is invested at 8.5% compounded monthly?
(1+(.085/12))^(12*1)=1.0884-1=.0884=8.84%
What is the effective rate for money that is invested at 4.3% compounded monthly?
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$3000 is invested in an account that makes 3.1% interest compounded monthly. How much money will there be in 8 years?
3000(1+(.031/12))^(128)=3843.15 Put the WHOLE equation in the calculator*
A colony of pigs is decreasing by 6% per year in the woods behind my house. Initially, there were 120 pigs. Make an exponential equation to model this situation. How long will it be until the population is down to 40 pigs?
y=120(.94)^x
y=120(.94)^3=100 pigs
40=120(.94)
(40/120)=(120/120)(.94)^x
log(1/3)/log(.94)=17.76
The value of a certain stock has been increasing at a rate of 1.2% per month. Initially, the stock was valued at $36. Make an exponential equation to model this situation.
How much is the stock worth in 5 months? How many months will it take for the stock to double in value?
y=36(1.012)^x
y=36(1.012)^5=38.21
A population is growing by 75 people a year. If the initial population was 500, write an equation representing the data.
y=500(1.065)^x
A population is growing by 6.5% per year. If the initial population was 500, write an equation representing the data.
y=500e^.04t
A population is growing continuously by 4% per year. If the initial population was 500, write an equation representing the data.
y=3(7)+500
y=21x+500
A population is growing tripling every 5 years. If the initial population was 500, write an equation representing the growth per year.
y=500(3)^(t/5)
The number of users of a new networking site has been growing by 4.5% a month. Initially, there were 400 users. Write an equation to predict the growth in the number of users per month. After 5 months, how many users will there be? How long will it take for the number of users in 2200? Show you work 3 ways.
y=400(1.045)^x
y=4001.045)^5=498
Cesium-137 which is a radioactive by product of nuclear fusion, has a continuous decay rate of 2.9% a year. Write the equation models the decay of Cesium-137. After 4 years what percent of the Cesium-137 will be left? How long will it take for there to be 1/2 the original amount?
y=100e^-.0229t=91.2%
50=100e^-.0229*4
(50/100)=(100/100)e^-.0229t
(LN2)/-.0229=-30.27
The number of boa constrictors predicted to occupy the Everglades was 23000 in 2005, and 44000 in 2012. Let X be the number of years since 2005. Write a linear equation to model the data in years since 2005.
(4400-23000)/(12-5)=3000
y=3000x+23000
44000/23000=a^7
7^√1.91=1.0971
Y1=3000x+23000
Y2=44000
(7,44000)
The initial value was 45. The value is decaying continuously 4.5% a year.
y=45e^-.045t
The initial value was 45. The value is tripling every year.
y=45(3)^x
The initial value is 45. The value is growing by a rate of 25% every 5 years.
y=45(1.25)^(x/5)
The initial value was 45. The value is decreasing 15 every year.
y=-15x+45
The initial value is 45. The value is decreasing by 3.5% a year.
y=45(.965)^x
The half-life of the dye that is used in stress tests is 4 hours. A person absorbs 12 mg of the dye for the test. What is the hourly decay factor? What is the hourly decay rate?
y=C(1/2)^x/t
y=12(1/2)^(x/4)
DF=(1/2)^(1/4)=.8409
DR=.8409-1=-15.91%
You invest $ 4000 in an account paying 3.5% interest compounded quarterly. After 5 years, how much money will you have?
4000(1+(.035/4)^(5/4)
My college algebra class has 35 students when the semester starts. If the drop rate 4% per week, how many weeks will it take for my class to be down to 25 students? 3 ways.
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I have an account that has a continuous interest rate of 3.5% I year. I initially put in$600. How many years will it take for my account to double?
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Jay deposited $2500 in an account that offers 6% interest compounded quarterly. Find the amount of money I will be in the bank account after 30 years? What is the effective rate?
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A biological commonly is doubling in size every 9 days. To what size will a colony of 800 individuals grow in 36 days? What is the daily growth factor? What is the daily growth rate?
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A radioactive substance decays according to the formula Q(x)=200(.85)^x, where X is in years and Q is in grams. What is the initial amount of the substance? What is the decay Factor? What is the decay rate of Q as a percent? When will it be half the original amount? After 10 years, how much of the original substance will be left?
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A plant is growing continuously at 5.5% a month. Initially, the plant was 7 centimeters tall. Write an equation for the plants growth. In how many months will it double in size?
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