8.1 Exponential Growth

Learning Targets Students should be able to…  Graph exponential growth functions.

Go over Chapter 7 test

Warm-up/Introduction

Exponential function- involves the expression b x where b is a positive number other than 1.

Base is the number b in an exponential function.

Asymptote- is a line that a graph approaches as you move away from the origin. y = a b

Exponential growth function- is an exponential function in the form where a > 0 and b > 1.

Graph exponential growth functions using y = ab x - h + k xy Graph y = 3·2 x Make a table with x values 0 and 1 Plot the points and draw a curve that runs close to the x-axis and passes through the two points D: all real R: y > 0 Asymptote y = 0

Graph y = 3·4 x -1 xy xy 13 2 Make a table with x values 0 and 1 Begin by looking at the un shifted graph of y= 3·4 x Shift the two points right 1 D: all real R: y > 0 Asymptote y = 0

Graph y = 4·2 x xy xy Begin by looking at the un shifted graph of y= 4·2 x Make a table with x values 0 and 1 Shift the two points right 3 and up 1 D: all real R: y > 1 Asymptote y = 1

2. Use exponential growth models in real life When a real-life quantity increases by a fixed percent each year (or other time period), the amount y of the quantity after t years can be modeled by this equation: y = a(1 + r) t In this model, a is the initial amount and r is the percent increase expressed as a decimal. The quantity 1 + r is called the growth factor.

In 1980 wind turbines in Europe generated about 5 gigawatt-hours of energy. Over the next 15 years, the amount of energy increased by about 59% per year. 1.Write a model giving the amount E (gigawatt-hours) of energy t years after About how much wind energy was generated in 1984? E=5(1.59) t About 32 hours 2.Graph the model. 3.Estimate the year when 80 gigawatt-hours of energy were generated? About 5.98 near the end of 1985

You purchase a baseball card for $54 dollars. If it increases each year by 5%, write an exponential growth model. V = 54(1.05) t

Compound Interest Consider an initial principal P deposited in an account that pays interest at an annual rate r (expressed as a decimal) compounded n times per year. The amount A in the account after t years can be modeled by You deposit $1500 in an account that pays 6% annual interest. Find the balance after 1 year if the interest is compounded A. Annually B. Semi-annually C. Quarterly =1590 = =

1.2. y = 2 x