1. Essential Question: How do you find a growth factor and a decay factor?

2.  An exponential function is a function with the general form y = ab x, with the following rules: ◦ a ≠ 0 ◦ b > 0 and b ≠ 1 ◦ x is a real number  When b > 1, b is called the growth factor

3.  Graphing Exponential Growth ◦ Example: Graph y = 2x ◦ Step 1: Make a table of values ◦ Step 2: Graph the coordinates with a smooth curve x2x2x y -32 -31 / 8 = 0.125 -22 -21 / 4 = 0.25 2 -11 / 2 = 0.5 02020 1 12121 2 22 4 32323 8

4.  If you know the rate of increase r, you can find the growth factor by using the equation b = 1 + r ◦ Example: In 2000, the population was 281 million and the annual rate of increase in the US population was about 1.24%. Suppose that increase continues to be 1.24%. Which function best models US population growth, in millions, after 2000? a)281 + 1.0124 x Hints: b)281(1.24) x c)281(1.024) x d)281(1.0124) x #1) Remember the form y = ab x #2) What is 1.24% written as a decimal?

5.  Using the function from the previous slide ◦ y = 281(1.0124) x ◦ Predict the US population in 2015 to the nearest million  ◦ Suppose the rate of population increase changes to 1.4%. Write a function to model population growth and then use it to predict the 2015 population to the nearest million.  281(1.0124) 15 ≈ 338 million 281(1.014) 15 ≈ 346 million

6.  An exponential function is a function with the general form y = ab x, with the following rules: ◦ a ≠ 0 ◦ b > 0 and b ≠ 1 ◦ x is a real number  When 0 < b < 1, b is called the decay factor

7.  Without graphing, determine whether the function y = 14(0.95) x represents exponential growth or exponential decay ◦  Y OUR T URN : Without graphing, determine whether the following functions represent exponential growth or exponential decay ◦ y = 100(0.12) x ◦ y = 0.2(5) x ◦ y = 16(½) x Since b < 1, this function represents exponential decay Exponential decay Exponential growth Exponential decay

8.  Assignment ◦ Page 434 – 435 ◦ Problems 1 – 9, 17 – 31 (odd problems)