Write each expression as a sum or difference of logarithms. All variables are positive. 4) log ( ) 843 6) Solve for x: 8 2x+3 = 467

Transcription

1 Write each expression as a single logarithm: 10 Name Period 1) 2 log 6 - ½ log 9 + log 5 2) 4 ln 2 - ¾ ln 16 Write each expression as a sum or difference of logarithms. All variables are positive. 3) ln x 2 y 3 z 8 x 4) log ( ) y 7 5) Evaluate: log ) Solve for x: 8 2x+3 = 467 7) Find the formula for the exponential function whose graph is shown in the figure: 8) Determine a formula for the exponential function shown in the table: x f(x) (0, 9) (2, 4)

2 -2-9) 235 grams of a radioactive substance is put in a container and left there for 130 days. At that time, only 204 grams of the original substance remains. Find its half-life: 10) The half-life of carbon-14 is 5730 years. A fossil is found, and it only contains 39% of the C-14 levels that current living creatures have. Approximately how old is the fossil? 11) Describe how to transform the graph of y = ln x into the graph of y = 11 - ln (x - 9) 12) A local deer population can be approximated by the following model based on data collected in 2000, with t representing the number of years since then. P(t) = e t Based on this model (a) what was the deer population in 2003? (b) what will the deer population be in 2018? (c) what is the maximum sustainable deer population?

3 -3-13) The population of Blue Falls is 17,511 and is growing by 0.85% each year. How long will it take Blue Falls to reach 25,000 people? 14) How many orders of magnitude are there between 30 and 300,000? 15) How many times stronger is an earthquake measuring 8.2 on the Richter scale than one measuring 5.8? 16) How many times more acidic is acid rain (ph = 5.2) than distilled water (ph = 7.0)? 17) Solve for x. Round to three places: 18) Solve for x: 3 4x+5 = 90 ln (2x + 1) + ln (x + 2) = ln 7 + ½ ln 4

4 -4-19) A pizza is taken out of an oven at 400 o F. After sitting in a 71 o F room for 11 minutes, its temperature was 250 o F. How warm would the pizza be if it sat in this room for an additional seven minutes? Round to three places: 20) In #19, approximate the temperature of the pizza after 17 days: 21) $6,123 is deposited into a bank offering a 1.95% interest rate compounded daily. Find the account balance after 12 years, assuming no withdrawals have been made during that time: 22) A bank offers a CD earning 3.5% interest, compounded quarterly. If you currently have $215 and want it to grow to $300, how long will you need to leave your money in the account?

5 -5-23) The value of an investment doubles every 20 years. How long would it take to triple? Compute the annual percentage yield (APY) of each investment. All calculations must be shown: 24) 5.6% interest compounded weekly 25) 1.3% interest compounded continuously 26) Morgan borrows $98,000 for a home mortgage. She is offered a fixed APR of 4.4% for 30 years. What will her monthly payment be?

6 -6-27) Desmond puts $75 into a savings account at the end of each month. If the account earns 1.8% annual interest, how long will he need to do this in order for the account balance to reach $20,000? 28) Find the y-intercept and the horizontal asymptotes for the following logistic equation: f(x) = e -2.3x ANSWERS: 1) log 60 2) ln 2 11) translate 9 units right, reflect across x-axis, translate 11 units up 19) o F 20) 71 o F 3) 2 ln x + 3 ln y + ½ ln z 4) ⅛ log x - 7 log y 5) ) x = ) y = 9 (2/3) x 8) y = 42 (1/3) x 10) 7, years 12) (a) 72 deer (b) 505 deer (c) 915 deer 13) years 14) 4 15) times stronger 16) times more acidic 9) days 17) x = ) x = 3/2 21) $7, ) years 23) years 24) 5.757% 25) 1.308% 26) $490.75/month 27) months or years 28) y-int: (0, 6) horiz. asymp: y = 0, y = 30