Linear and Exponential Functions

A population of 200 worms increases at the rate of 5 worms per day. How many worms are there after a fifteen days? Linear Function

Exponential Growth A population of 200 worms increases at the rate of 5% per day. How many worms are there after fifteen days?

Linear Functions Slope m=rise/run Slope m=rise/run Change on y when x increases by 1 Y intercept or value when x=0

Exercise Find the equation of the line passing through the points (-2,1), (4,5) Point: Slope: Point-Slope form Slope-Y intercept form

Exercise 3 A car is 30 kilometers away from a city and start moving at a constant velocity of 50 km/hour. – Generate a table to determine the distance from the city during the first 4 hours, recording the information every half and hour (∆t = 0.5) – Find a mathematical expression that represents the distance of the car from the city as a function of time, in hours. – Use the mathematical expression to determine: How far the car is after 3.5 hours. How long it takes the car to be 135 km away from the city.

Exponential Growth Population of Mexico City since 1980 (t=0) Initial Population t=0 Grows at 2.6% per year (100%+2.6% next period) = growth factor 1= Grows at 2.6% per year (100%+2.6% next period) = growth factor 1=

Exercise 4 A population can be modeled by the expression – What is the initial population? – What is the growth factor for this population? – What is the rate of growth per year of this population? – What is the rate of growth every four year?

Exponential Decay Amount of carbon-14 present after t years. Initial amount (t=0) Decay factor = Decay rate 0.013% Decay factor = Decay rate 0.013%

Dominance Exponential growth dominates any power function as x goes to infinity