Unit 3 Exam Review

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1.
Expand the following logarithmic expression:
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2.
Expand the following natural log expression:
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3.
Condense the following log expression:
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Solve the following inequality:

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5.
Solve the following inequality in terms of natural logarithms (ln).


6.
Solve forxin the following equation:
  1. x= 1
  2. x= 2
  3. x= 8
  4. x= -4

7.
What is the solution set forxin the logarithmic equation log3(x- 9) - log3x= 3?

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8.
Solve the following logarithmic equation forx.
log5(x+ 5) - log5(2x- 6) = log53
  1. -
  2. -3
  3. 3

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9.
The Fein family needs to have $35,000 available in 18 years when their son is ready for college.If they have decided to invest in a mutual fund that compounds interest continuously at 5.2%, how much money do they need to invest now to reach their goal?
  1. $13,726.77
  2. $1,372.67
  3. $15,349.20
  4. $1,534.92

/ 10.
A logarithmic function of base ‘3’ has a vertical asymptote at the linex= 1. Its graph contains the point (2, 1). What is the equation of the function?
  1. f(x) = log3(x+ 1)
  2. f(x) = log3(x- 1) + 1
  3. f(x) = log3(x+ 1) + 1
  4. f(x) = log3(x) + 1

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11.
What is the equation of the function graphed below?

  1. f(x) = ln(x- 2) + 3
  2. f(x) = log(x- 2) + 3
  3. f(x) = ln(x+ 2) + 3
  4. f(x) = log (x+ 2) + 3

12.
Condense the following expression:
  1. ln 3e
  2. lne3
  3. ln 3e3
  4. lne2+e

13.
The table shows measurements of a rocket launched from a submarine and hitting the radar tower of an enemy airbase. The radar tower is located at sea level. Find an equation that best models the data in the table, and answer the following questions.

aWhat is the maximum height of the rocket, to the nearest
hundredth of a foot?
Answer:feet
bTo the nearesttenth of a second, when will the rocket hit its target?
Answer:sec
cTo the nearesttenth of a second, for what period of time is the rocket at an altitude above 2,000 feet?Answer:sec
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Zoe is a manager at a local diner.She keeps records of daily purchases by the customers to help predict how much food to purchase each week.Lately, Zoe has been paying special attention to the orders of corned beef.She knows that from Sunday to Saturday, the number of meals per day of corned beef increases.Her problem is that she does not work on Tuesdays or Thursdays.Based on the table below, with Sunday being day 1, predict, to the nearest meal, the number of corned beef dinners needed for Tuesday and Thursday of each week.Use the line of best fit to help predict the number of meals.

aFind the equation for the line of best fit to the nearest tenth.
y=x+
bUsing the equation in parta, find the number of meals needed for Tuesdays.
Answer:meals
cUsing the equation in Parta, find the number of meals needed for Thursdays.
Answer:meals
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15.
A player on a football team was practicing his punts. The coaches took precise measurements as to time and height of the ball.The table below shows the measurements taken by the coaches, where time is the independent variable and height is the dependent variable.

aUsing a quadratic regression, find the best approximation for the equation of the path of the football, rounding all the coefficients to thenearest hundredth.
y=x2+x+
bBased on the equation in parta, what is the height of the ball at 2.25 seconds, to the nearest foot?
Answer: feet
cThe maximum height of the ball, to the nearest tenth of a foot, isfeet, and it takesseconds (rounded to the nearest tenth of a second) to reach that height.
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Sean invests $10,000 at an annual rate of 5% compounded continuously, according to the formulaA=Pert, whereAis the amount,Pis the principal,e= 2.718,ris the rate of interest, andtis time, in years.
Determine, to thenearest dollar, the amount of money Sean will have after 2 years.Answer: $
Determine how many years, to thenearest year,it will take for Sean’s initial investment to double.Answer:years
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17.
Jean invested $380 in stocks. Over the next 5 years, the value of her investment grew, as shown in the accompanying table.

Write the exponential regression equation for this set of data, rounding all values totwo decimal places.
Answer: y=()x
Using this equation, find the value of her stock, to thenearest dollar,10 years after her initial purchase.
Answer: $
18.
The table shows a set of data.

What type of regression best fits the scatter plot of this data?
  1. Power
  2. Linear
  3. Exponential
  4. Logarithmic

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What type of regression does the scatter plot below best represent?

  1. Linear
  2. Quadratic
  3. Exponential
  4. Power

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20.
What type of regression does the scatter plot below best represent?

  1. Linear
  2. Exponential
  3. Logarithmic
  4. Power

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21.
What type of regression does the scatter plot below best represent?
  1. Linear
  2. Exponential
  3. Logarithmic
  4. Power

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22.
The table below shows the results of an experiment involving the growth of bacteria.

Which power regression equation is correct for this set of data, rounding all values tothree decimal places?
  1. y= 2.01x2.3
  2. y= 2.001x2.298
  3. y= 2.001x.298
  4. y= 2.001x2.398

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23.
The following table shows the estimated yearly electricity usage in kilowatt-hours and the estimated yearly operating costs in dollars for energy efficient refrigerators.

To the nearest dollar, what would be the estimated yearly operating cost of a refrigerator with a yearly electricity usage of 630 kWh?
  1. $77
  2. $72
  3. $69
  4. $67

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24.
The table shows the number of tomato plants planted at a farm since 1990.

Find a cubic model to estimate the number of tomato plants planted in 2005.
  1. 1394.7 thousand
  2. 1249.6 thousand
  3. 1132.9 thousand
  4. 978.6 thousand

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25.
Akeem invests $25,000 in an account that pays 4.75% annual interest compounded continuously. Using the formulaA=Pert, whereA= the amount in the account aftertyears,P= principal invested, andr= the annual interest rate, how many years, to thenearest tenth, will it take for Akeem’s investment to triple?
  1. 10.0
  2. 14.6
  3. 23.1
  4. 24.0

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