Natural Growth and Decay
Compounded Continuously
Percent inc. / dec. Compound Interest
Annuities / Amortization
Miscellaneous & Exponential Regression
100
In a community, the original population has 20 dogs. After 3 years, the population has grown to 87 dogs. Write an equation giving the population for any year.
P(t) = 20 (1.63241)^t
100
If I invest $300 into an account compounded continuously with a rate of 3.6% for 4 years, how much will I end with?
$346.47
100
Margaret bought a dress that was originally $54.00 If this dress was on sale for 30%, how much did she actually pay for it?
$37.80
100
$250 is invested each month into an account compounded monthly with a rate of 4.6%. After 4 years, how much money is in the account?
$13147.37
100
When do you use the APY formula?
When the question asks for effective rate. Or when the question asks for a comparison of two rates
200
A population of gerbils grows from 112 to 347 in 5 months. Write an equation giving the population for any month.
P(t) = 112 (1.25378)^t
200
I invest $800 into an account compounded continuously with a rate of 20% (whoa!) for 2 years. How much interest did I make?
$393.46
200
Jimmy Neutron emptied his piggy bank today and found $22.58. If he invests this money into an account that is compounded monthly with a rate of 4.2%, how much money will he have after 3 years?
$25.61
200
Sally takes out a loan for $120,000. If her bank offers her a 20 year loan compounded monthly with a rate of 2.7%, what will her monthly payments be?
$647.64
200
An exponential model has the following points: (0,5), (1,7), (2,10), (3,15), (4,23). Find the exponential model that best fits the data. When x is 5, what is y?
y = 4.846 (1.46437)^x When x is 5, y is 32.61
300
Poachers are beginning to hunt a population of wildebeests! :( The population started at 115 and 5 wildebeests are killed every 6 months. Write a model showing the population of wildebeests for any month.
P(t) = 115 (.99262)^t
300
If I invest $200 into an account compounded continuously with a rate of 4.6%, how long will it take for my account to reach $850?
31.5 years
300
Alexis was online shopping and bought a new purse for $87.49 (including sales tax). If sales tax was 7.25%, how much did the purse originally cost before sales tax was added?
$81.58
300
Michael puts $200 into an account each month for 18 years towards his son's 'college fund'. This account has a rate of 4.5% compounded monthly. If 1 school year at UTA costs $15,000, does he have enough money for his son to attend 4 years?
Yes! The account will have $66373.60. Only $60,000 is needed.
300
Sam invests money into an account that is compounded monthly with a rate of 4%. According to the 'Rule of 72', how long will it take for Sam's money to quadruple?
36 years
400
A population of giraffes grows from 410 to 682 in 8 months. What will the population be after 3 years?
4049 giraffes
400
$1100 is entered into an account compounded continuously with a rate of 3.4%. How long will it take for the money to double?
20.4 years
400
A classroom has 14 girls in it. If 80% of the class are boys, how many boys are in the classroom?
56 boys
400
John takes out a loan for his $67,000 boat. His bank offers him a 15-year loan compounded quarterly with a rate of 6.4%. What are his periodic payments? After 15 years, how much did he actually spend on his boat?
$1745.40 (4 times a year) $104724.00
400
The following data was collected for the population of Lewisville. (1970,1223), (1975, 1391), (1980, 1663) where the y value is in thousands of people. A. Find the best fitting exponential model B. Predict the population for 1996 C. Approximately how long will it take the population to reach 1,800,000. What year is this?
A. 1212.874(1.03121)^x B. 2,696,750 C. 1982
500
The Loch Ness Monster and his family and friends have been discovered! If this population increases from 5 to 12 sea monsters in 11 months, when will there be 22 sea monsters?
18.6 months
500
An account is compounded continuously with a rate of 4%. How long will it take for the amount to quadruple?
34.7 years
500
Mark invests $1200 into an account that is compounded quarterly with a rate of 6.4%. How long will it take for his account to have $1900?
7.24 years
500
Jace got a loan of $100,000 from the bank after paying 12% of the selling price as a down payment. The 10-year loan had a rate of 3.9% compounded monthly. How much was the down payment? How much interest did he pay?
Down payment = $13,636.36 Interest he paid for house = $20,925.20
500
The data for the cost of a shoe chain are given as follows. (16,4.8), (22,5.9), (35,7), (48,9), (53,10), (70,12), (100,18), (150,30) where the x values are the output in hundreds of pairs of shoes and the y-values are the total cost in thousands of dollars A. Determine the best fitting exponential function B. What is the cost for producing 9000 pairs of shoes? C. How many shoes can be produced for $25,000?
A. Y = 4.4667(1.01343)^x B. $14,845.96 C. 12,905 shoes
M
e
n
u