Extra Practice – Exponentials and Logarithms
Solve the following equations (you may leave logs in your answer):
1. 2. 3. 4. 5.
6. 7. 8. 9.
10. 11. 12.
13. 14. 15.
16. 17. 18.
19. 20. 21.
22. 23. 24.
25. A colony of bacteria grows exponentially. The colony begins with 3 bacteria, but 6 hours after the beginning of the experiment, it has grown to 24 bacteria.
a) Find a formula for the number of bacteria as a function of time (in hours).
b) How long will it take the colony to reach 300 bacteria?
26. A rubber ball is dropped onto a hard surface from a height of 2 meters, and it bounces up and down. After each bounce it rises to 90% of the height from which it fell.
a) Find a formula for h(n), the height reached after n bounces.
b) How high will the ball bounce on the 12th bounce?
c) How many bounces before the ball rises no higher than 1 cm?
27. Scientists observing owl and hawk populations collect the following data. Their initial count for the owl population is 245 owls, and the population seems to grow by 3% each year. They initially observe 63 hawks, and this population doubles every 10 years.
a) Find a formula for the size of the population of owls in terms of time.
b) Find a formula for the size of the population of hawks in terms of time.
c) Approximately when will the two populations be equal in number?
28. If 17% of a radioactive substance decays in 5 hours, what is its half-life?
29. Suppose a colony of bacteria is known to grow exponentially with time. At the end of 3 hours there are 10,000 bacteria. At the end of 5 hours there are 40,000. How many bacteria were present initially?
30. The total number of hamburgers sold by a national fast-food chain is growing exponentially. If 4 billion had been sold by 2001 and 6 billion had been sold by 2006, how many will have been sold by 2011?
Extra Practice – Exponentials and Logarithms – Answers
1. 2. 3. 4.
5. 6. 7. 8.
9. 10. 11.
12. 13. 14. 15.
16. 17. 18. 19. 20.
21. 22. 23. 24.
25a. 25b.
26a. 26b. 26c.
27a. 27b. 27c.
28.
29. 1250 bacteria
30. 9 billion hamburgers