APPLICATIONS (a) Find an exponential model n(1) = n,2lª for the number of bacteria in the culture after 1 hours. 1-16 - Population Growth These exercises use the population growth model. (b) Estimate the number of bacteria after 18 hours. (c) After how many hours will the bacteria count reach 1 million? 1. Bacteria Culture A certain culture of the bacterium Strepto- coccus A initially has 10 bacteria and is observed to double every 1.5 hours. (a) Find an exponential model n(1) = no2la for the number 3. Squirrel Population A grey squirrel population was intro- duced in a certain county of Great Britain 30 years ago. Biologists observe that the population doubles every 6 years, and now the population is 100,000. of bacteria in the culture after 1 hours. (b) Estimate the number of bacteria after 35 hours. (a) What was the initial size of the squirrel population? (c) After how many hours will the bacteria count reach (b) Estimate the squirrel population 10 years from now. (c) Sketch a graph of the squirrel population. 10,000? 4. Bird Population A certain species of bird was introduced in a certain county 25 years ago. Biologists observe that the population doubles every 10 years, and now the population is 13,000. (a) What was the initial size of the bird population? (b) Estimate the bird population 5 years from now. (c) Sketch a graph of the bird population. 5. Fox Population The fox population in a certain region has a relative growth rate of 8% per year. It is estimated that the population in 2013 was 18,000. (a) Find a function n(1) = noe" that models the population I years after 2013. (b) Use the function from part (a) to estimate the fox popula- tion in the year 2021. (c) After how many years will the fox population reach 25,000? Streptococcus A (12,000 × magnification) 2. Bacteria Culture A certain culture of the bacterium Rhodo- bacter sphaeroides initially has 25 bacteria and is observed to double every 5 hours. (d) Sketch a graph of the fox population function for the years 2013–2021. © Sebastian Kaulitaki/ Shutterstodk.com