EOC Review:Explicit & Recursive

Exponential functions match geometric sequences

y = a(b)x

initial value rate of change(y-intercept)

•NEXT = b(NOW)

• Starting value for recursive form is the first term – not y-intercept.

Try creating a table to visualize the patterns.

• NEXT = 2(NOW) starting at -4

• y = _____ (2)x

• Find the y-intercept by reversing the table.

Example: E#4.1• A geometric sequence is shown: 32, 16, 8, ...

• Which is the explicit formula for this sequence?• What is the recursive formula?• What is the 6th term?

How do we know it is exponential?

Example E#4.2The recursive formula NEXT = 4 • NOW models the number of people with a virus in a school each week. If there are 36 people infected with the virus after 3 weeks, how many people will be infected after 6 weeks? What is the explicit formula?

How do we know this is exponential?

You Try!• Try making a table to check your patterns & formulas.

Check it E#4.3The explicit formula A = 2(3)n models the growth of a colony of bunnies in a year. What is the recursive formula for this?

Check it: E#4.4• A sequence is shown: 2, 6, 18, 54, . . .

• Which recursive formula models the sequence?• What is the explicit formula for the sequence?• What is the 10th term?

Check it: E#4.5The recursive formula for a sequence is shown below. NEXT = 2 • NOW, starting at 4Which explicit formula can be used to determine the value of the nth term in the sequence?What is the 6th term in the sequence?

Check it E#4.6• The explicit formula for a geometric sequence is A =

5(1/2)x .• What is the recursive formula?• What is the 5th term in the sequence?