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Exponential and Logistic Modeling
Determine the exponential function with initial value = 12, increasing at a rate of 8% per year.
Initial mass = 15 g, decreasing at a rate of 4.6% per day
Initial value = 5, decreasing at a rate of 0.59% per week
Initial population = 502,000, increasing at a rate of 1.7% per year
Suppose a culture of 100 bacteria is put into a petri dish and the culture doubles every hour. Predict when the number of bacteria will be 350,000.
Suppose the half-life of a certain radioactive substance is 20 days and there are 5 grams present initially. Find the time when there will be 1 g of the substance remaining.
Use the table of data and exponential regression to predict the US population for Compare the result with the listed value for U. S. Population (in millions) YearPopulation
Pg. 296 – 298, #’s: 1, 2, 8, 17, 22, 25, 32, 39, 44, 53, 54 Total Problems: 11
Constant Rate Exponential Population Model Date: 3.2 Exponential and Logistic Modeling (3.2) Find the growth or decay rates: r = (1 + r) 1.35% growth If.
Exponential Functions Chapter 1.3. The Exponential Function 2.
Exponential Modeling Section 3.2a. Let’s start with a whiteboard problem today… Determine a formula for the exponential function whose graph is shown.
Pg. 282/292 Homework Study #7$ #15$ #17$ #1x = 2 #2x = 1#3x = 3 #4x = 4 #5x = -4 #6x = 0 #7no solution #8x = 2 #9Graph #10Graph #11Graph.
Chapter 1.3 Exponential Functions. Exponential function F(x) = a x The domain of f(x) = a x is (-∞, ∞) The range of f(x) = a x is (0, ∞)
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Warm Up: Find the final amount : Invest $4000 at 6% compounded quarterly for 20 years. Invest $5600 at 3.7% compounded continuously for 12 years.
ACTIVITY 40 Modeling with Exponential (Section 5.5, pp ) and Logarithmic Functions.
Quiz This data can be modeled using an exponential equation exponential equation Find ‘a’ and ‘b’ 2.Where does cross the y-axis ? 3. Is g(x)
Various Forms of Exponential Functions M is the total number after time t. c is the initial amount at time t = 0. d is the doubling period t is the time.
Quiz 3-1a 1.Write the equation that models the data under the column labeled g(x). 2. Write the equation that models the data under the column labeled.
Section 4.2 Logarithms and Exponential Models. The half-life of a substance is the amount of time it takes for a decreasing exponential function to decay.
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Exponential Growth and Decay Section 3.5. Objectives Solve word problems requiring exponential models.
Algebra 2. The _______________ number …. is referred to as the _______________________. An ___________ function with base ___ is called a __________.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 3.1 Exponential and Logistic Functions.
Objective: Use exponential and logarithmic models to solve real life problems. 3.5 Exponential & Logarithmic Models 2014.
1 Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 3.1 Exponential Functions Demana, Waits, Foley, Kennedy.
Growth and Decay Exponential Models. Exponential Growth Function n(t)=n 0 e kt, k>0 or n(t)=n 0 a t, a>1 n 0 = initial amount=n(0) a = growth factor n(t)
Exponential Growth and Decay; Modeling Data. 1. The exponential model describes the population of a country, A in millions, t years after Use this.
4.8 Exponential and Logarithmic Models. Exploring - 3 Exponential Models Uninhibited Growth/Decay Exponential growth/decay with limiting factors Logistic.
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Pg. 259/245/68 HW Review Pg. 255#6, 14, 24, 28, 35, 51 Pg. 268#1, 3, 5 – 9 odd, 15 #58#59 ft/sec #60#61t = sec #62 V(t) = 36πt 3 #63V(5) = 14,
Pg. 255/268 Homework Pg. 277#32 – 40 all Pg. 310#1, 2, 7, 41 – 48 #6 left 2, up 4#14Graph #24 x = #28x = 6 #35 Graph#51r = 6.35, h = 9, V = 380 #1 Graph#3a)
Section 3.2b. In the last section, we did plenty of analysis of logistic functions that were given to us… Now, we begin work on finding our very own logistic.
Section 6.2 Exponential Function Modeling and Graphs.
Warm-up Identify if the function is Exp. Growth or Decay 1) 2) Which are exponential expressions? 3)4) 5)6)
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Directions Put your name at the top of a blank sheet of paper. There are 11 word problems around the room. You may start at any problem and do not have.
MATH 109 Test 2 Review. Jeopardy Show me the $$$$$ Exponential Applications Famous Log Cabins Potpourri
Whether does the number e come from!?!?. Suppose the number of bacteria, n 0, in a dish doubles in unit time. If a very simple growth model is adopted,
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Exponential Growth and Decay 6.4. Exponential Decay Exponential Decay is very similar to Exponential Growth. The only difference in the model is that.
Worksheet/Pg. 269/277 Homework Pg. 282#7, 15, 17 Pg. 292#1 – 20 all #50 81,920; 2.31x10 19 #51P(t) = 20(2) t # months#53food, health, etc #
Quiz 3-1a 1.This data can be modeled using an exponential equation exponential equation Find ‘a’ and ‘b’ 2.Where does cross the y-axis ? 3. Is r(x)
Honors Precalculus: Do Now Solve for x. 4 2x – 1 = 3 x – 3 You deposit $7550 in an account that pays 7.25% interest compounded continuously. How long will.
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EXPONENTIAL GROWTH Exponential functions can be applied to real – world problems. One instance where they are used is population growth. The function for.
Pg. 255/268 Homework Pg. 277#32 – 40 all Pg. 292#1 – 8, 13 – 19 odd #6 left 2, up 4#14Graph #24 x = #28x = 6 #35 Graph#51r = 6.35, h = 9, V = 380 #1 Graph#3a)
Applications of Exponential Functions. Radioactive Decay Radioactive Decay The amount A of radioactive material present at time t is given by Where A.
Modeling Constant Rate of Growth (Rate of Decay) What is the difference between and An exponential function in x is a function that can be written in the.
Rates of Growth & Decay. Example (1) The size of a colony of bacteria was 100 million at 12 am and 200 million at 3am. Assuming that the relative rate.
Section 3.5 Exponential and Logarithmic Models. Compound Interest The compound interest formula: A is the amount in the account after t years. P is the.
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