✓ Got It?

1. What is the graph of each function?
   1. y = 4 x y equals , 4 to the x
   2. y = ( 1 3 ) x y equals . open , 1 third , close to the x
   3. y = 2 ( 3 ) x y equals 2 open 3 , close to the x
   4. Reasoning What generalizations can you make about the domain, range, and y-intercepts of these functions?

Dynamic Activity

Exponential Growth and Decay

Take Note Concept Summary: Exponential Functions

For the function y = a b x , y equals eh , b to the x , comma

• if a > 0 eh greater than 0  and b > 1 , b greater than 1 comma  the function represents exponential growth.
• if a > 0 eh greater than 0  and 0 < b < 1 , 0 less than b less than 1 comma  the function represents exponential decay.

In either case, the y-intercept is (0, a), the domain is all real numbers, the asymptote is y = 0 , y equals 0 comma  and the range is y > 0 . y greater than 0 .

Problem 2 Identifying Exponential Growth and Decay

Identify each function or situation as an example of exponential growth or decay. What is the y-intercept?

1. y = 12 ( 0.95 ) x y equals 12 open , 0.95 , close to the x

   Since 0 < b < 1 , 0 less than b less than 1 comma  the function represents exponential decay. The y-intercept is (0, a) = (0, 12).

2. y = 0.25 ( 2 ) x y equals , 0.25 , open 2 , close to the x

   Since b > 1 , b greater than 1 comma  the function represents exponential growth. The y-intercept is (0, a) = (0, 0.25).

3. You put $1000 into a college savings account for four years. The account pays 5% interest annually.

   The amount of money in the bank grows by 5% annually. It represents exponential growth. The y-intercept is 1000, which is the dollar value of the initial investment.

✓ Got It?

2. Identify each function or situation as an example of exponential growth or decay. What is the y-intercept?
   1. y = 3 ( 4 x ) y equals 3 open , 4 to the x , close
   2. y = 11 ( 0.75 x ) y equals 11 open , 0.75 to the x , close
   3. You put $2000 into a college savings account for four years. The account pays 6% interest annually.