1. 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= ) r= ) r= 2.015

2. Exponential day 3

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.

4. 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

5. 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

6. 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.

7. Practice in Class
Page 394: #15-18

8. Homework
394: # Due Friday