Homework Check 5.51. In year 2 there are 40 lizards2. In year 1 there are 20 lizards3. At about 3.5 years4. and this continues

5. 10

6. Keep multiplying by 2 each year.

Recall:

•All arithmetic sequences are LINEAR FUNCTIONS

•All geometric functions are EXPONENTIONAL FUNCTIONS

IndiaLong ago in India, there lived a raja who believed

that he was wise and fair. But every year he kept nearly all of the people’s rice for himself. Then when famine came, the raja refused to share the rice, and the people went hungry. Then a village girl named Rani devises a clever plan. She does a good deed for the raja, and in return, the raja lets her choose her reward. Rani asks for just one grain of rice, doubled every day for thirty days. Through the surprising power of doubling, Rani teaches the raja a lesson about what it truly means to be wise and fair.

•y = the number of bacteria produced in that hour

•r = b = the common ratio or rate of change

•x = the number of hours

•a1 = a = the initial term of the sequence or the starting point

A and B

A is your starting valueB is growth factorX is timeY is the amount after time

Time to create an equation for Exponential (geometric) functions!

Exponential FunctionsAn exponential function is a function with the general form

y = abx

a ≠ 0 and b > 0, and b ≠ 1

Starting Value and Growth FactorIdentify each starting value and the growth factor.1. Y= 3(1/4)x

2. Y= .5(3)x

3. Y = (.85)x

Looking at the Grain of RiceThis is an exponential function.What was our equation be?

Was our x value the number of days?

What does x represent?

Modeling Exponential FunctionsSuppose 20 rabbits are taken to an island. The rabbit population then triples every year. The function f(x) = 20 • 3x where x is the number of years, models this situation. What does “a” represent in this problems? “b”?

How many rabbits would there be after 2 years?

Modeling Exponential FunctionsSuppose a Zombie virus has infected 20 people at our school. The number of zombies doubles every day. Write an equation that models this.

How many zombies are there after 5 days?

If there are 1800 students at Knightdale, how long will it take for the Zombie virus to infect the whole school?

3. A Bacteria culture doubles in size every hour. The culture starts at 150 cells.  How many will there be after 6 hours?

After 24 hours?

4. A population of 2500 triples in size every year.  What will the population be in 5 years?

HW

•5.6