University:
Florida Gateway College
Course:
BSC 2010C | General Biology I with Lab
Academic year:

2021
Views:

229

Pages:

2
Author:

agenciafocozo

Pre-Calculus 4.4-4.5 Applications D2 Worksheet Name:________________________ For #1 – 4, use the exponential growth model: 𝒏(𝒕) = 𝒏𝟎 𝒆𝒓𝒕 1. The number of bacteria in a culture is modeled by the function 𝑛(𝑡) = 500𝑒 0.45𝑡 where 𝑡 is measured in hours. a. How many bacteria are in the culture after 3 hours? b. After how many hours will the number of bacteria reach 10,000? 2. The population of a certain city was 112,000 in 1998 and the observed relative growth rate is 4% per year. In what year will the population reach 200,000? 3. A certain breed of rabbit was introduced onto a small island about 9 years ago. The current rabbit population on the island is estimated to be about 4,700, with a relative growth rate of 35% per year. 4. a. What was the initial size of the rabbit population? b. Estimate the population 11 years from now. Hint: If you are looking 11 years from now, how long has it been since the initial time? A culture contains 1,500 bacteria initially and doubles every 30 minutes. a. Find a function that models the number of bacteria at time 𝑡. b. Find the number of bacteria after two hours. c. After how many minutes will there be 4,000 bacteria? 𝒕 For #5-6, use the radioactive decay model: 𝒂(𝒕) = 5. 6. 𝟏 𝒌 𝒂𝟎 (𝟐) Radium-226 has a half-life of 1,600 years. Suppose a sample of this substance has a mass of 22 mg. a. Find a function that models the amount of the sample remaining at time 𝑡. b. Find the mass remaining after 4,000 years. The half-life of Strontium-90 is 28 years. How long will it take a 50 mg sample to decay to a mass of 32 mg? For #7-8, use Newton’s Law of Cooling: 𝑻(𝒕) = 𝑻𝒔 + 𝑫𝒐 𝒆−𝒌𝒕 7. 8. A hot bowl of soup is served at a dinner party. It starts to cool according to Newton’s Law of Cooling so that its temperature at time 𝑡 is given by 𝑇(𝑡) = 65 + 145𝑒 −0.05𝑡 where 𝑡 is measured in minutes and 𝑇 is measured in ℉. a. What is the temperature of the soup after 10 minutes? b. After how long will the temperature be 100 ℉? A cup of coffee has a temperature of 205℉ and is placed in a room that has a temperature of 75 ℉. After 12 minutes, the temperature of the coffee is 165 ℉. a. Find a function that models the temperature of the coffee at time 𝑡. b. Find the temperature of the coffee after 15 minutes. 1a. 1928.7 1b. 6.66 hrs 2. 2012 4b. 23986 4c. 42.4 min. 5a. 𝑎(𝑡) = 22 (2) 8a. 𝑇(𝑡) = 75 + 130𝑒 −0.0306𝑡 3a. 201 rabbits 1 8b. 157.15° 𝑡 1600 3b. 220,423 (or 220,867) 5b. 3.89 mg 6. 18 yrs 4a. 𝑛(𝑡) = 1500𝑒 0.0231𝑡 7a. 152.95° 7b. 28.4 min

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