Warm-UP Convert the following rates to decimals 50% 2) 245% 3) 17% 50% 2) 245% 3) 17% Convert the following rates to percentages 4) r= 0.042 5) r=1.87 6) r= 2.015

Exponential day 3

Exponential models of population growth 𝑛 𝑡 = 𝑛 0 𝑒 𝑟𝑡 or 𝐴 𝑡 =𝑃 𝑒 𝑟𝑡 𝑛 0 𝑖𝑠 𝑡ℎ𝑒 𝑖𝑛𝑖𝑡𝑎𝑙 𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 just like P was the initial amount or principal. 𝑛 𝑡 𝑖𝑠 𝑡ℎ𝑒 𝑓𝑖𝑛𝑎𝑙 𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 just as 𝐴(𝑡) was the final amount.

Example The initial count in a culture is 500. A biologist later makes a sample count of bacteria in the culture and finds that the relative rate of growth is 40% per hour. a) Find a function that models the number of bacteria after t hours b) What is the estimated count of the function after 10 hours c) Sketch the graph of the function 𝑛 𝑡

Comparing rates In 2000 the population of the world was 6.1 billion and the relative rate of growth was 1.4%. It is claimed that a rate of 1.0% per year would make a significant difference in the total population in just a few decades. Test this claim by estimating the population of the world in 2050 using a rate of growth for 1.4% per year 1% per year

Finding initial amounts A certain breed of rabbit was introduced onto a small island about 8 years ago. The current rabbit population on the island is estimated at 4100, with a relative growth rate of 55% per year? a)What is the initial size of the population? b) Estimate the population 12 year from now.

Practice in Class Page 394: #15-18

Homework 394: # 19-27 Due Friday