Download Lesson 4.8 – Exponential Growth and Decay

Lesson 4.8 – Exponential Growth and Decay
1) A colony of bacteria grows according to the law of uninhibited growth. If 100 grams of bacteria are present initially, and 250
grams are present after two hours, how many will be present after 4 hours?
2) The half-life of Uranium-234 is 200,000 years. If 50 grams of Uranium-234 are present now, how much will be present in 1000
years (Half-life is the time required for half of a radioactive substance to decay).
3) An initial deposit is made in a savings account for which the interest is compounded continuously. The balance of the account
will quadruple in 80 years. When will the balance of the account reach $41,000 if the initial deposit was $8,000?
4) A colony of bacteria starts with 100 bacteria and increases according to the law of uninhibited growth.
a) If the number of bacteria doubles in 3 hours, find the function that gives the number of cells in the culture.
b) How long will it take the size of the colony to triple?
c) What is the population of the bacteria after 8 hours?
5) The logistic growth model P (t ) 
500
represents the amount of bacteria (in grams) after t days
1  6.67e 0.2476t
a) What is the carrying capacity?
b) What was the initial amount of bacteria?
c) When will the amount of bacteria be 300 grams?
Lesson 4.8 – Exponential Growth and Decay
1) A colony of bacteria grows according to the law of uninhibited growth. If 100 grams of bacteria are present initially, and 250
grams are present after two hours, how many will be present after 4 hours?
2) The half-life of Uranium-234 is 200,000 years. If 50 grams of Uranium-234 are present now, how much will be present in 1000
years (Half-life is the time required for half of a radioactive substance to decay).
3) An initial deposit is made in a savings account for which the interest is compounded continuously. The balance of the account
will quadruple in 80 years. When will the balance of the account reach $41,000 if the initial deposit was $8,000?
4) A colony of bacteria starts with 100 bacteria and increases according to the law of uninhibited growth.
a) If the number of bacteria doubles in 3 hours, find the function that gives the number of cells in the culture.
b) How long will it take the size of the colony to triple?
c) What is the population of the bacteria after 8 hours?
5) The logistic growth model P (t ) 
500
represents the amount of bacteria (in grams) after t days
1  6.67e 0.2476t
a) What is the carrying capacity?
b) What was the initial amount of bacteria?
c) When will the amount of bacteria be 300 grams?