7-1&7-2 story problems review.notebook - moore public schools · 71&72 story problems...

71&72 story problems review.notebook

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January 11, 2018

Jan 118:15 AM

Thursday, January 11Bell Work

1.a. Does the function represent exponential growth ordecay? How do you know?

b. What is the parent function?

c. Describe any transformations on the parent graph.

d. What is an asymptote?

e. Where is the asymptote?

Jan 118:19 AM

On

Worksheet


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January 11, 2018

Jan 239:37 AM

Jan 128:00 AM

1. From 1997 to 2002, the number n (in millions) of DVD players sold in the United States can be modeled by n = 0.42(2.47)t where t is the number of years since 1997.a. Identify the initial amount, the growth factor, and the annual percent increase.

b. Graph the function. Estimate the number of DVD players sold in 2001.


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January 11, 2018

Jan 128:01 AM

2. Each March from 1998 to 2003, a website recorded the number of y of referrals it received from Internet search engines. The results can be modeled by y = 2500(1.5)t where t is the number of years since 1998.a. Identify the initial amount, the growth factor, and the annual percent increase.

b. Graph the function and state the domain and range. Estimate the number of referrals the website received from Internet search engines in March of 2002.

Jan 128:09 AM

3. You deposit $2200 in a bank account. Find the balance after 4 years for each of the situations described below.

a. The account pays 3% annual interest compounded quarterly.

b. The account pays 2.25% annual interest compounded monthly.

c. The accounts pays 2% annual interest compounded daily.


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January 11, 2018

Jan 128:02 AM

5. In 1990, the population of Austin, Texas was 494,290. During the next 10 years, the population increased by about 3% each year.

a. Write a model giving the population P(in thousands) of Austin t years after 1990. What was the population in 2000?

b. Graph the model and state the domain and range.

c. Estimate the year when the population was about 590,000.

Jan 128:03 AM

6. At an online auction, the opening bid for a pair of inline skates is $50. The price of the skates increases by 10.5% per bid during the next 6 bids.

a. Write a model giving the price p (in dollars) of the skates after n bids.

b. What was the price after 5 bids? According to the model, that will the price be after 100 bids? Is this predicted price reasonable? Explain


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January 11, 2018

Jan 252:47 PM

Jan 128:06 AM

11. You buy a new mountain bike for $200. The value of the bike decreases by 25% each year.

a. Write a model giving the mountain bike’s value y (in dollars) after t years. Use the model to estimate the value of the bike after 3 years.

b. Graph the model.

c. Estimate when the value of the bike will be $100.


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January 11, 2018

Jan 128:08 AM

15. The number E of eggs of Leghorn chicken produces per year can be modeled by the equation E = 179.2(0.89)w/52 where w is the age (in weeks) of the chicken and w ≥ 22a. Identify the decay factor and the percent decrease.

b. Graph the model.

c. Estimate the egg production of a chicken that is 2.5 years old.

d. Explain how you can rewrite the given equation so that time is measured in years rather than in weeks.

Jan 239:38 AM


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January 11, 2018

Jan 129:12 AM

1. From 1997 to 2002, the number n (in millions) of DVD players sold in the United States can be modeled by n = 0.42(2.47)t where t is the number of years since 1997.

a. Identify the initial amount, the growth factor, and the annual percent increase.

b. Graph the function. Estimate the number of DVD players sold in 2001.

2. Each March from 1998 to 2003, a website recorded the number of y of referrals it received from Internet search engines. The results can be modeled by y = 2500(1.5)t where t is the number of years since 1998.

a. Identify the initial amount, the growth factor, and the annual percent increase.

b. Graph the function and state the domain and range. Estimate the number of referrals the website received from Internet search engines in March of 2002.

3. You deposit $2200 in a bank account. Find the balance after 4 years for each of the situations described below.

a. The account pays 3% annual interest compounded quarterly.


c. The accounts pays 2% annual interest compounded daily.

4. You want to have $3000 in your savings account after 3 years. Find the amount you should deposit for each of the situations described below.

a. The account pays 2.25% annual interest compounded quarterly.


c. The accounts pays 4% annual interest compounded yearly.

Jan 129:13 AM

5. In 1990, the population of Austin, Texas was 494,290. During the next 10 years, the population increased by about 3% each year.

a. Write a model giving the population P(in thousands) of Austin t years after 1990. What was the population in 2000?

b. Graph the model and state the domain and range.

c. Estimate the year when the population was about 590,000.

6. At an online auction, the opening bid for a pair of inline skates is $50. The price of the skates increases by 10.5% per bid during the next 6 bids.

a. Write a model giving the price p (in dollars) of the skates after n bids.

b. What was the price after 5 bids? According to the model, shat will the price be after 100 bids? Is this predicted price reasonable? Explain

7. In 2000, the average price of a football ticket for a Minnesota Vikings game was $48.28. During the next 4 years, the price increased an average of 6% each year.

a. Write a model giving the average price p (in dollars) of a ticket t years af ter 2000.

b. Graph the model. Estimate the year when the average price of a ticket was about $60.

c. Explain. How you can use the graph of p(t) to determine the minimum and maximum pvalues over the domain for which the function gives meaningful results.

8. In 1977, there were 41 breeding pairs of bald eagles in Maryland. Over the next 24 years, the number of breeding pairs increased by about 8.9% each year.

a. Write a model giving the number n of breeding pairs of balk eagles in Maryland t years after 1977.

b. Make a table of values for the model.

c. Graph the model.

d. About how many breeding pairs of bald eagles were in Maryland in 2001?


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January 11, 2018

Jan 129:17 AM

1. Is investing $3000 at 6% annual interest and $3000 at 8%annual interest equivalent to investing $6000 (the total of the twoprincipals) at 7% annual interest (the average of the two interestrates)? Explain

2. When a person takes a dosage of I milligrams of ibuprofen, theamount A (in milligrams) of medication remaining in theperson’s bloodstream after t hours can be modeled by theequation A + I(0.71)t.

Find the amount of ibuprofen remaining in a person’sbloodstream for the given dosage and elapsed time since themedication was taken.

a. Dosage: 200mg b. Dosage : 325mgc. Dosage: 400mg

Time: 1.5 hours Time: 3.5 hours Time: 5 hours

3. You buy a new mountain bike for $200. The value of the bikedecreases by 25% each year.a. Write a model giving the mountain bike’s value y (in dollars)after t years. Use the model to estimate the value of the bikeafter 3 years.

b. Graph the model.

c. Estimate when the value of the bike will be $100.

4. The table shows the amount d that a boat depreciates duringeach year t since it was new. Show that the ratio of depreciationamounts of consecutive years is constant. Then write anequation that fives d as a function of t.

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Jan 129:18 AM

13. The value of a car can be modeled by the equation y = 24,000(0.845)t where t is the number of years since the car was purchased.

a. Graph the model. Estimate when the value of the car will be $10,000.

b. Use the model to predict the value of the car after 50 years. Is this a reasonable value? Explain.

14 When a plant or animal dies, it stops acquiring carbon14 from the atmosphere. Carbon14 decays over time with a halflife of about 5730 years. The percent P of the original amount of carbon14 that remains in a sample after t years is given by this equation:

P = 100(½)t/5730

a. What percent of the original carbon14 remains in a sample after 2500 years? 5000 years? 10,0000?

b. Graph the model?

c. An archaeologist found a bison bone that contained about 37% of the carbon14 present when the bison died. Use the graph to estimate the age of the bone when it was found.

15. The number E of eggs of Leghorn chicken produces per year can be modleed by the equation E = 179.2(0.89)w/52 where w is the age (in weeks) of the chicken and w ≥ 22

a. Identify the decay factor and the percent decrease.

b. Graph the model.

c. Estimate the egg production of a chicken that is 2.5 years old.

d. Explain how you can rewrite the given equation so that time is measured in years rather than in weeks.

16. A species of extremely rare, deep water fish are slowly becoming extinct. If there are a total of 821 of this type of fish and there are 15% fewer fish each month, how many will there be in half a year?

17. A mouse population is 25,000 and is decreasing in size at a rate of 20% per year. What is the mouse population after 3 years?


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January 11, 2018

Aug 231:22 PM

Section 7-1 & 7-2

QUIZ REVIEW

Objective: Using Exponential growth and decay models.

Thursday, January 11

Jan 118:12 AM

1.a. Does the function represent exponential growth ordecay? How do you know?

b. What is the parent function?

c. Describe any transformations on the parent graph.

d. Where is the asymptote?

2.


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January 11, 2018

Jan 118:22 AM

Use the graph of y = 2(1/2)x + 2 for questions 3 and 4.

1. 5.What is domain of y = 2(1/2)x + 2?

2. What is the range of y = 2(1/2)x + 2?

3. & 4.

Jan 118:22 AM

1. The value of a car y (in thousands of dollars) can be approximately by the model y = 22(.75)t, where t is the number of year since the car was new.

a. Identify the following:

Initial amount: ________________

Growth factor: ________________

Annual percent of decrease: ______

b. What is the value of the car after 3 years?

c. Estimate when the value of the car will be $5,300?

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January 11, 2018

Jan 118:22 AM

#61. The population of kangaroos in central Australia has decreased drastically in the past two years. The rate of decrease is about 2%, and the current population is 1400 kangaroos.

a. Write a model giving the population P of kangaroos after t years.

At this rate, what will the kangaroo population be in 10 years?

Jan 118:25 AM

#71. You deposit $1500 in an account that pays 2.5% annual interest. What is the balance after 5 years if the interest is compounded with the given frequency?

a. Daily?

b. Semi‐annually?

c. Quarterly?

d. Monthly?

A = P(1 + )ntr

n


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January 11, 2018

Jan 117:59 AM

Joke of the day!!!What’s the difference between a horse and the

weather?

One is reined up

and

the other rains down.

Jan 118:27 AM

QUIZ

Tomorrow!!


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January 11, 2018

Jan 118:29 AM

Jan 118:29 AM


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January 11, 2018

Jan 118:29 AM

7-1&7-2 story problems review.notebook - moore public schools · 71&72 story problems...

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