1 The following model can be used to show the probability for how often a customer arrives at a drive up window:

P(t)=1-e^(-0.2t)

Determine the probability of arriving at t=5.

Determine the probability of arriving at t=10.

Graph the function.

2 Determine if a linear or exponential model is better for the following functions by graphing these functions and adding trendlines and R^2.

a) X F(X)

-1 3

0 6

1 12

2 18

3 30

b) X F(X)

-1 0.25

0 1

1 4

2 16

3 64

c) X F(X)

-1 2

0 4

1 6

2 8

3 10

3 Graph the following functions:

a) Y = 3^X

b) Y = -3^(-X)

c) Y = e^X

d) Y = 1-3^X

4 If 4^X=7, what does 4^(-2X) equal?

5 If 3^(X-2)=2, what does 3^(2X) equal?

6 The price P(X) of a car that is X years old is:

P(x)=16630*(0.90)^X

How much does the car cost is X = 3 years?

How much does the car cost is X = 9 years?

Graph this function.

What year will the car reach $5000?

7 Solve the following equations for X:

a) e^(2X)=5

b) 20=6*e^(12.77*X)

c) 100=6*e^(-2*X)

8 Population P(t) equation follows:

P(t)= 298,710,000+10,000,000*LN (t).

Find t =1,10, and 20.

Graph this function.

9 Car Depreciation

New t =0 t=1 t=2 t=3 t=4 t=5

$38,000 36,600 32,400 28,750 25,400 21,200

Use the formula:

New=Old*e^(r*t)

Find the value of rate, r for a specific time, t.

Graph your function.

Compute the trendline and R^2.

0 1 2 3 4 5 6 7

10 Year 2006 2007 2008 2009 2010 2011 2012 2013

Sales 132.1 157.4 184.4 212.6 241.5 272.1 278.8 284.3

Let X =0 in 2006.

a) Build a model of the data by graphing it, using a trendline and R^2.

b) Estimate sales in 2015 and 2018.

c) Graph the exponential model from a).

11 When money is placed n a bank account that pays compound interest, the amount grows exponentially.

Suppose such an account grows from $1000 to $1316 in 7 years.

a. Find a growth function of the form f(t) = Yo*e^(rt)

f(0) 1000

f(7) 1316

1316=1000e^(r*t)

ln(1316/1000)=r*t

ln(1316/1000)/t=r

b. What is the value of rate, r?

c. How much is in the account in 12 years?

12 Infant mortality in USA is shown in the following table:

Year Rate Year Rate

1920 76.7 1980 12.6

1930 60.4 1985 10.6

1940 47 1990 9.2

1950 29.2 1995 7.6

1960 26 2000 6.9

1970 20 2005 6.9

a. Let t=0 correspond to 1920.Use the data from 1920 to 2005

to find a function to model f(t)=Yob^t

6.9=76.7e^(r*85)

general model:

Y =Yoe^(rt)

b. Graph the model above.Insert an exponential trendline.How does the trendline model compare ?

c. Use your model to predict the mortality rate in 2006 and 2012.

t(86) 2006

t(92) 2012

13 Sales of new products often grow rapidly at first and begin tolevel off in time.

Suppose the annual sales of an inexpensive good are given by:

S(X)=10000(1-e^(-0.5X)

where X = 0 corresponds to the time the good went on the market.

a. What were the sales in each of the first three years?

b. What were the sales at the end of the 10th year X = 10?

c. Graph the function S(X)=10000(1-e^(-0.5X))

14 Suppose you owe $800 on your credit card and you decide to make no new purchases

and to only make the minimum monthly payment on the account.

Assuming that the interest in the card is 1% per month on the unpaid balance and the minimum payment is 2%

of the total balance (balance plus interest), your balance after t months is modeled as:

B(t)=800(0.9898)^t

a. Using the above model, findyour balance at the endo of 6 months

b. One year (t = currently in months)

c. Five years

d. 8 years

15 The amount spent on health care in the USA is approximated by:

H(t)=ho*1.065^t

where t = 0 corresponds to year 2000 and H(t) is in thousands of dollars.

a. The amount spent per person on healthcare in 2000 was $4624.Find ho.

b. Find the healthcare costs per person in years 2008, 2010, and 2012.

c. Graph the function.

16 The table below shows the purchasing power of a dollar in recent years,

with 2000 equal to the base year.

a. Find an exponential model for the data where t=0 corresponds to 2000.

b. Find the purchasing power of a dollar in 2010, 2012, and 2014.

c. In what year will the dollar drop in purchasing power to 0.40 cents?

d. Graph the function you modeled.

YEAR Purchasing Power of $1

2000 $1.00

2001 0.97

2002 0.96

2003 0.94

2004 0.91

2005 0.88

2006 0.85

2007 0.83

2008 0.79

17 Assembly line operations tend to have a high t turnover of employees, forcing companies

to spend more time and effort, and cost to train new employees.It is found, in one firm, that

a worker who is new to production will produce P(t) items on day t, and can be modeled by:

P(t)=25-25e^(-0.3t)

a. How many items will be produced on the first day?

b. How many items will be produced on the 8th day?

c. What is the maximum number of items that can be produced according to this function?

d. Graph the productivity function.

18 The number of words per minute that an average college student can type is given by:

W(t)=60-30e^(-0.5t)

where t is the number of months after beginning typing lessons.

a. Find W(0)

b. Find W(4)

c. Find W(6)

19 Outstanding consumer credit in billions of dollars is shown in the following table:

YEAR CREDIT OUTSTANDING

1980 $350.5

1985 524.0

1990 797.7

1995 1010.4

2000 1543.7

2005 2200.1

2006 2295.4

2008 2535.6

a. Develop an exponential model for the data, using t =0 corresponds to 1980.

b. What will outstanding credit be in 2013 and 2016?

c. In what year will outstanding credit reach $6000 billion?

20 Since 2000, the national debt can be modeled like:

f(X)= 40.35/(1+6.39e^(-0.0866X))

where X =0 correspondsto year 2000 and f(X) is measured in trillions of dollars.

a. Estimate the national debt in 2000, 2010, and 2015.

b. Graph f(X) from above from 2000 to 2050.

c. What year will the debt reach $20 trillion?