DO NOW 3 1 Exponential and Logistic Function

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DO NOW 3. 1 Exponential and Logistic Function

DO NOW 3. 1 Exponential and Logistic Function

DO NOW 3. 1 Exponential and Logistic Function

DO NOW 3. 1 Exponential and Logistic Function

DO NOW 3. 1 Exponential and Logistic Function

DO NOW 3. 1 Exponential and Logistic Function

OBJECTIVE 3. 2 Exponential Modeling Use exponential • SWBAT growth and decay to model

OBJECTIVE 3. 2 Exponential Modeling Use exponential • SWBAT growth and decay to model real-life problems.

KEY CONCEPT Exponential Population Model Suppose r: a constant percentage rate Find the exponential

KEY CONCEPT Exponential Population Model Suppose r: a constant percentage rate Find the exponential population model function by completing a table. Time in years 0 1 2 3 t Population

DEFINITION Exponential Population Model

DEFINITION Exponential Population Model

EXAMPLE 1 Finding growth and decay rates Tell whether the population model in an

EXAMPLE 1 Finding growth and decay rates Tell whether the population model in an exponential growth function or exponential decay function, and find the constant percentage rate of growth or decay.

EXAMPLE 2 Finding an exponential function Determine the exponent function with initial value=12, increasing

EXAMPLE 2 Finding an exponential function Determine the exponent function with initial value=12, increasing at a rate of 8% per year.

EXAMPLE 3 Modeling Bacteria Growth Suppose a culture of 100 bacteria is put into

EXAMPLE 3 Modeling Bacteria Growth Suppose a culture of 100 bacteria is put into petri dish and the culture doubles every hour. Predict when the number of bacteria will be 350, 000.

EXAMPLE 4 Modeling Radioactive Decay Suppose the half-life of a certain radioactive substance is

EXAMPLE 4 Modeling Radioactive Decay Suppose the half-life of a certain radioactive substance is 20 days and there are 5 g present initially. Find the time there will be 1 g of substance remaining.

EXERCISE 1 The 2000 population of Las Vegas, Nevada was 478, 000 and is

EXERCISE 1 The 2000 population of Las Vegas, Nevada was 478, 000 and is increasing at the rate of 6. 28% each year. At that rate, when will the population be 1 million?

EXERCISE 2 The population of River City in the year 1910 was 4200. Assume

EXERCISE 2 The population of River City in the year 1910 was 4200. Assume the population increased at a rate of 2. 25% per year. (a) Estimate the population in 1930 and 1945. (b) Predict when the population reached 20, 000.

EXERCISE 3 The half-life of a certain radioactive substance is 14 days. There are

EXERCISE 3 The half-life of a certain radioactive substance is 14 days. There are 6. 6 g present initially. (a) Express the amount of substance remaining as a function of time t. (b) When will there be less than 1 g remaining?

HOMEWORK 3. 2 Exponential and Logistic Modeling p. 270 -272 #2, 4, 6, 8,

HOMEWORK 3. 2 Exponential and Logistic Modeling p. 270 -272 #2, 4, 6, 8, 10, 12, 20, 22