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

An exponential function is a function with the general form y = abx, 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

Graphing Exponential Growth◦ Example: Graph y = 2x◦ Step 1: Make a table of values◦ Step 2: Graph the coordinates

with a smooth curve

x 2x y

-3 2-3 1/8 = 0.125

-2 2-2 1/4 = 0.25

-1 2-1 1/2 = 0.5

0 20 1

1 21 2

2 22 4

3 23 8

2 4–2–4 x

2

4

6

8

y

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 + 1.0124x Hints:b) 281(1.24)x

c) 281(1.024)x

d) 281(1.0124)x

#1) Remember the form y = abx

#2) What is 1.24% written as a decimal?

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

An exponential function is a function with the general form y = abx, 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

Without graphing, determine whether the function y = 14(0.95)x represents exponential growth or exponential decay◦

YOUR TURN: 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

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