A) How Long Will It Take for the Investment to Be Worth $150?

0.201t 1. The speed of a barge after time, t, in seconds is given by V  Vo 10 where is the speed when the engines are stopped. Calculate the speed after 3 seconds, if the speed of the barge is 12km.h at the time when the engines are stopped.

2. An investment of $100 is made is a term deposit that pays 16% pa compounded annually. The value A, of the investment in dollars after time, t, in years, is given by A  100(1.16)t . a) How long will it take for the investment to be worth $150? b) How long will it take to double the value of the investment?

3. In 1976 a research hospital bought half a gram of radium for cancer research. Assuming the hospital still exists, how much of this radium will the hospital have in the year 6836 if the half life of radium is 1620 a?

t 4. The number of cells in a culture grows according to the equation A  2500(10) 4 , where A is the number of cells after time, t, in seconds. How long will it take the number of cells to grow to 1.3108 ?

5. A cloth, made from plant material was found intact during the excavation of a tomb. The amount of C14 in the cloth was 2.7 g. The original amount of C14 was 3.8 g. What is the age of the cloth? (½ life =5760 a)

6. Phoebe Small is out driving in her rocket ship. She fills up with fuel and takes off. When she starts the last stage of her rocket, she is going 4230 miles per hour (mph). Ten seconds later she is going 6850 mph. While the last stage is running, you may assume that Phoebe’s speed increase exponentially with time. In order to go into orbit, Phoebe must be going 17 500 mph. a) What is the minimum length of time the last stage could run and still get Phoebe into orbit? b) How long would the last stage have to run to get Phoebe going 25 000 mph so that she could go off the Moon?

7. Assume that whenever you wash a pair of blue jeans, they lose 4% of the color they had just before they were washed. a) Explain why the percent of the original color left in the blue jeans varies geometrically with the number of washings. What is the common ratio? b) How much of the original color would be left after 10 washings? c) Suppose that you buy a new pair of blue jeans, and decide to wash them enough times so that only 25% of the original color remains. How many times must you wash them? d) Explain why an arithmetic sequence would not be a reasonable mathematical model for the amount of color left after many washings?