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Exponential Regressionsand

Test Review

Exponential Models for data…• In a research experiment, a population of fruit flies was

introduced into an environment and recorded below.

Elapsed time

(in days)

Population of fruit flies

0 252 286 33

10 3915 4919 5924 7430 96

1) Use your calculator to write an exponential model to best fit the data and PASTE it into Y=

2) Use your model to predict the number of fruit flies after 40 days.

3) Use your model to determine the elapsed time when then population of fruit flies was 65.

Time (L1)

Temp (L2)

1 184.35 164.07 155.1

10 143.714 130.518 119.920 115.223 109.2628 101

Time (L1)

Temp (L2)

32 95.72838 89.5645 84.3650 81.6260 77.8370 75.5380 74.1488 73.43

100 72.78

• A temperature probe was placed in a cup of hot coffee then removed and held in a room that was 70°. The temperature of the probe was recorded below.

TRASHKETBALL

Test Review

1) Determine a function for the

logistic function whose graph

is shown in the figure.

2) What is the total value after 6 years

of an initial investment of $2250 that

earns 7% APR compounded quarterly?

CALCULATOR ACTIVE

The population of a town is 350,000 and is increasing at the rate of 4.65% every year.

1. Write a function that determines the population of the town in terms of the number of years.

2. After how many years will the population be one million? (Round to 3 decimal places)

3. What will be the population in 30 years?

1. The half life of a certain substance is 60 days. How much of 24 grams will be left after 100 days?

2. How long will it take an account that compounds continuously at 6% APR to double in value?

3. A certain account has accumulated $10,000 in 5 years. The account has earned 4%APR compounded monthly. What was the initial deposit?

CALCULATOR ACTIVE

Calculator ActiveThe table shows the population of

Aurora, CO for selected years between 1950 and 2003.

1. Use logistic regression to find a logistic curve to model the data. Write your model rounding to 3 decimal places.

2. Based on the regression equation, what is the carrying capacity of Aurora, CO.? (3 decimal places)

3. Based on the regression equation, after how many years will the population exceed 300,000? (3 decimal places)

4. Based on the regression equation, what was the (approximate) population in 1965?

(nearest whole number).

Years after 1950

Population

0 11,421

20 74,974

30 158,588

40 222,103

50 275,923

53 290,418

NO Calculator

Solve for x:

1. log4256 = x

2.

3.

1log 2

4x

1

125

4log

3x

NO Calculator

5 5 5

11) log 3log 4 log 64

3 x

62 log2) 6 9x

12 12 12

13) 2log log 9 3log 3

2 x

NO Calculator1) logb1 = x

2

12) log

b xb

3) Simplify completely2 3ln e x

NO Calculator

Solve for x:

1. log2x2 – log2(x+3) = 2

2. log4x + log4(x – 3) = log77

1. Write as a single logarithm:

2. Write as simplified logarithms

1log log( 1) log(2 )2

x x x

2

2log

1

x

x

Solve for x. NO CALCULATOR

1) 2 + 3e-x = 8 2) 3e2x + 8ex = 3

Solve for x. NO CALCULATOR

1) 8x+1 = 10 2)

xe 5.41

3010

xe 5.41

3010

Calculator ActiveThe winning times in the women’s 100 meter freestyle event at the Summer Olympic Games since 1952 are shown. Let x = 0 be 1900…

1) Assuming the data approaches a horizontal asymptote of y = 52, write an exponential model that best fits the data.

2) According to this model, what would be the winning time for the women’s freestyle at the 2008 Olympics? Round to 3 decimal places.

YearsSince 1900

52 56 60 68 72 76 80 84 88 92 96 100

Time 66.8 62 61.2 60 58.6 55.7 54.8 55.9 54.9 54.6 54.5 53.8