Analysis Name______Exponential Growth and Decay IV Date______

1. A certain experiment with bacteria begins with 2000 bacteria. Two hours later, there are 3000 bacteria. Assuming continuous growth, find the growth constant k, and the time it will take the population to reach 5000.

2. Another population of bacteria grows in such a way that it will double in three hours. Assuming continuous growth, how long will it take for the number of bacteria to reach seven times the original number of bacteria?

3. As part of his summer job at a restaurant, Jim learned to cook up a big pot of soup late at night, just before closing time, so that there would be plenty of soup to feed customers the next day. He also found out that, while refrigeration was essential to preserve the soup overnight, the soup was too hot to be put directly into the fridge when it was ready. (The soup had just boiled at 100 degrees C, and the fridge was not powerful enough to accommodate a big pot of soup if it was any warmer than 20 degrees C). Jim discovered that by cooling the pot in a sink full of cold water, (kept running, so that its temperature was roughly constant at 5 degrees C and stirring occasionally, he could bring the temperature of the soup to 60 degrees C in ten minutes. How long before closing time should the soup be ready so that Jim could put it in the fridge and leave on time?

4. The half-life of iodine-131 is eight days. How much of a one gram sample will remain after seven days?

5. At the start of an experiment, there are 100 bacteria. If the bacteria follow an exponential growth pattern with rate k = 0.02, (a) what will be the population after 5 hours? (b) how long will it take for the population to double?

6. Suppose that the population of a colony of bacteria increases exponentially at a continuous rate. At the start of an experiment, there are 6,000 bacteria, and one hour later, the population has increased to 6,400. How long will it take for the population to reach 10,000? Round your answer to the nearest hour.

Exponential Growth and Decay 4 John Cendrowski Lower Moreland HS Analysis Exponential Growth and Decay IV Page 2

7. The half-life of Plutonium-239 is 24,000 years. If 10 grams are present now, how long will it take until only 10% of the original sample remains? Round your answer to the nearest 10,000th.

8. Suppose that at the start of an experiment there are 8,000 bacteria. A growth inhibitor and a lethal pathogen are introduced into the colony. After two hours 1,000 bacteria are dead. If the death rates are exponential and continuous,

(a) how long will it take for the population to drop below 5,000?

(b) How long will it take for two-thirds of the bacteria to die? Round your answers to the nearest tenth.

9. Suppose some environmental stress reduced a population of 1000 wee beasties to 800 in two days. How many will there be 7 days after the initial count of 1000 wee beasties?

10. Suppose you put one bacterium on a petri plate containing a suitable medium at a favorable temperature. Assume that there will be a doubling every 20 minutes. How many would you expect to find after 6 hours?

11. The half-life of Carbon-14 is 5730 years. A piece of ancient charcoal contains only 15% of its original amount of Carbon-14. How long ago was the tree burned to make the ancient charcoal?

12. The population of bacteria in a culture is growing exponentially. At 12:00 there were 80 bacteria present and by 4:00 PM there were 500 bacteria. Find an exponential function f(t) = ae kt that models this growth, and use it to predict the size of the population at 8:00 PM.

Growthanddecay4 Mr. John Cendrowski Lower Moreland High School