HW: pg ,10,14,26-28 Do Now: Take out your pencil, notebook, and calculator. 1) Objectives: You will be able to define exponential functions. You will be able to graph exponential functions. You will be able to determine if an exponential function is growth or decay. You will be able to model and solve problems for exponential growth and decay. Agenda: 1.Do Now 2.Exponential functions mini lesson 3. Homework How do you model and exponential function? Wednesday February 11, 2015

7.1 –Exponential Functions An exponential function has the general form y = ab x where a=0 and b>0 and b= 1. ExponentConstant Base

Graphing Exponential Functions Example 1:Graph y = 2 x

Graphing Exponential Functions Example 2:Graph y = 9(1/3) x

2 Types of Exponential Functions For exponential growth, as the value of x increases, the value of y increases. For exponential decay, as the value of x increases, the value of y decreases, approaching zero. The exponential functions shown are asymptotic to the x-axis. An asymptote is a line that a graph approaches as x or y increases but never touches. For exponential functions this the x- axis.

Types of Exponential Functions <b For the function If 0<b<1 then exponential decay If b>0 then exponential growth Y-intercept is always (0, a)

Exponential Functions Example 3: Identify each function or situation as an example of exponential growth or decay and determine the y-intercept. 1.f(x) = 12(0.95) x 2. f(x) =.25(2) x 3. You put $1000 into a college savings account for four years. The account pays 5% interest annually.

Why exponential functions???? We need exponential functions in the real world because they help us model money (saving money, losing money etc.) They also help us model population (i.e. determine the population size of a country after so many years).

7.1 –Exponential Functions Exponential Growth Models A(t) = a(1+r) t Exponential Decay Models A(t) = a(1-r) t Rate of growth (r > 0) or decay (r < 0) Number of Periods Initial amount Amount after t time periods

Example 5: Modeling Exponential Growth-annual interest You invested $1000 in a savings account at the end of 6 th grade. The account pays 5% annual interest. How much money will be in the account after 6 years? 9 years? When will the account have $3000?

Example 6: Modeling exp. growth If the rabbit population is growing at a rate of 20% every year and starts out at 150 rabbits currently. a. How many rabbits are there in 12 years? b. How long does it take for the population to reach 5000 rabbits?

Example 7: Modeling Exp. Decay The population of a certain animal species decreases at a rate of 3.5% per year. You have counted 80 of the animals in the habitat you are studying. a.Write a function that models the change in the animal population. b.Graph the function. Estimate the number of years until the population first drops below 15 animals.

7.1 –Exponential Functions Compound Interest

Example 9: You deposit $4000 in an account that pays 2.92% annual interest. Find the balance after 3 years if the interest is compounded with the given frequency. a.Quarterly b.Daily

Example 10: You want $2000 in an account after 4 years. Find the amount you should deposit for each of the situations described below. a.The account pays 2.5% annual interest compounded quarterly. b.The account pays 3.25% annual interest compounded monthly.