Honors Pre Calculus Worksheet 3.1. A. Find the exponential equation for the given points, and then sketch an accurate graph (no calculator). 2.

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1 Honors Pre Calculus Worksheet 3.1 A. Find the eponential equation for the given points, and then sketch an accurate graph (no calculator). 1., 3, 9 1,. ( 1, ),, B. Sketch a graph the following logistic growth functions. Label all intercepts and asymptotes (no calculator) f( ) = g= ( )

2 C. Match each of the following functions with their graphs (no calculator) 1. f( ) = a b c d 1. f( ) + = ( 1) 3. f( ) + = f( ) = 3-5. f( ) = f( ) = e f g h 7. f( ) = f( ) = 9. f( ) = 3( ). f( ) = i j D. Answer the following questions using the population models. 1. After hours, a biologist has a sample of 3 bacteria. After hours, the sample has 79 bacteria. Find an eponential model for this situation, then estimate the amount of bacteria after hours.. The number of sheep in Ireland can be estimated by the logistic function below, where t is the number of years after f() t = 0.131t e What was the number of sheep in 1819? About how many sheep were there in the year 1850? How long will it take to triple the number of sheep?

3 Honors Pre Calculus Halldorson 3.: Properties of Logarithm Functions 1. Use your calculators to re epress the data in the table to the right using the natural log function. Distance (meters) Force (Newtons) Ln(d) Ln(F) ( ) d ( ) ln( F) =.001 ln( ) (for our purposes r is the same as d).90 ( ) ln( F) =.001 ln( d) + ln e ln( F) = ln d + ln e ( )( ) ln F = ln d e F = e d F = = d G d ( 18.83) ( )( ) r.90 m kg s 3 11 G

4 HCP PRECALC In-Class WS NAME CALCULATORS ALLOWED 1. A casserole is removed from a 5 F oven, and it cools to 50 F after 15 minutes in a 75 F room. How long (from the time it is taken out of the oven) kt does it take to cool to 90 F? (Hint: Tt () = T + ( T T) e ) m o m. The half-life of a certain radioactive substance is hours. There are grams present initially. a. Epress the amount of substance remaining as a function of time t. State the units for t. b. When will there be 1 gram remaining? 3. Find the eact solution(s) algebraically. Check graphically. (a) 5 = (b) ln(3+ ) ln(+ 1) = 5

5 . It s not been a good week in Papua, Indonesia. On Friday, November 8, they eperienced an earthquake measuring 7.1 on the Richter scale. On Sunday, November 30, they eperienced an earthquake measuring. on the Richter scale. How many times more severe was the first earthquake than the second? 5. How long will it take an investment of $850 at 8.5% APR compounded quarterly to grow to $00?. What is the annual percentage yield of an account paying 9.15% APR compounded monthly? (FORMULA TOO!!!) 7. Juan contributes $175 monthly into an IRA annuity for 0 years. If the account earns 5.% annual interest compounded monthly, what is the value of Juan s account after 0 years? (FORMULA TOO!!!) 8. A $130,000 mortgage requires monthly payment for 30 years at.5% APR. How much is each payment? (FORMULA TOO!!!)

6 HCP PRECALC Review Chapter 3 NAME CALCULATORS ALLOWED 1. The population of Glenbrook is 5,000 and is increasing at the rate of.5% per year. (a) Find an eponential equation that models this growth. State the units for t. (b) Use part (a) to predict when the population will be 1 million.. The half-life of a certain radioactive substance is days. There are 5 grams present initially. (a) Epress the amount of substance remaining as a function of time t. State the units for t. (b) When will there be 1 gram remaining? 3. Find the eact solution(s) algebraically. Check graphically. (a) = 8 (b) + e = (c) ln = 3. A pie is removed from a 375º F oven, and it cools to 00º F after 15 minutes in a 75º F room. How long kt (from the time it is taken out of the oven) does it take to cool to 0º F? (Hint: Tt () = T + ( T T) e ) m o m 5.

7 What is the annual percentage yield of an account paying.15% APR compounded quarterly?. Teddy contributes $150 monthly into an IRA annuity for 0 years. If the account earns.% annual interest compounded monthly, what is the value of Teddy s account after years? 7. A $5,000 mortgage requires monthly payment for 30 years at.8% APR. How much is each payment? NO CALCULATORS!! 1. Define e.. State the Fundamental Theorem of Algebra. 3. Simplify: 3 ln 3ln + ln e e e. Epress the following in epanded form (i.e., in terms of log and log y : 3 log 5 z 5. Consider the following function: f( ) = 3ln( ) a. State it s domain: b. State it s range: c. State it s range: d. Give the eact value of it s y-intercept:

8 d. Give the eact value for it s -intercept.. Solve: 3 7 = 3 7. Solve: log 5( ) = 1 8. Are the functions f ( ) ln = and g ( ) ln = equal? Eplain. 9. How is the graph of log ( 3 ) 1 5 related to the graph of ln?

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

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