7-1 Exponential Functions Today’s Objective: I can model exponential growth and decay.

Exponential Function 𝑦= 2 𝑥 𝑦=𝑎⋅ 𝑏 𝑥 𝑎≠0 y-intercept: (0, a) 0.0625 -4 -2 -1 1 2 3 𝑎≠0 y-intercept: (0, a) 0.0625 a = starting value 0.25 b = Constant Multiplier 0.5 𝑏>1 Growth 1 0<𝑏<1 Decay 2 4 Domain: All real #s 8 Range: 𝑦>0 Graph on calculator and sketch x-axis is an asymptote. a line a graph approaches 𝑦= 1 3 𝑥 𝑦= 4⋅2 𝑥 𝑦= 4 𝑥

Exponential Growth and Decay 𝑦=𝑎⋅ 𝑏 𝑥 You invest $1,000 in an account for 6 years at 5% annual interest. What is your balance? Amount after t time periods Initial Amount # of time periods 𝐴(𝑡)= ⋅ (1+ ) 1000 0.05 6 𝐴(𝑡)=𝑎⋅ (1+𝑟) 𝑡 =1000 (1.05) 6 Growth factor: r = % growth or decay written as a decimal Growth: 𝑟>0 Decay: 𝑟<0 =$1340.10

Exponential Growth and Decay 𝐴(𝑡)=𝑎⋅ (1+𝑟) 𝑡 You invest $500 in an account for 5 years at 3.5% annual interest. What is your balance? Jackson High school had 2,100 students at the start of the school year and it is predicted to decrease by 1.5% each year. How many students will be at Jackson at the start of the 2020 school year? 𝐴(𝑡)= ⋅ (1+ ) 5 500 0.035 =500 (1.035) 5 =$593.84 When will the account be worth $1,000? Use calculator table. 𝐴(𝑡)= ⋅ (1+ ) −0.015 5 2100 About 21 years =2100 (0.985) 5 =1,947 𝑦 1 =500 (1.035) 𝑥

Endangered Species 7-1 p.439: 10, 14, 18-31 If the trend continues and the population of the Iberian Lynx is decreasing exponentially, how many Iberian Lynx will there be in 2014? 𝑦=𝑎⋅ 𝑏 𝑥 120 150 𝑎= 150 𝑏= =0.8 𝑝(𝑡)=150⋅ (0.8) 𝑡 7-1 p.439: 10, 14, 18-31 𝑝(11)=150⋅ (0.8) 11 =12