Math 141, Sem. I, 1998-99 (R.A. Brualdi)
Handout 12 (October 19, 1998)
Topic: Ways to grow.
1. You and a friend are traveling down a road in different vehicles, both
beginning at 30 mph.
Vehicle A: Every hour the speed is increased by 5 mph (constant
acceleration of 5 mph^2).
Vehicle B: Every hour the speed is increased by 5%.
(a) For each vehicle, determine the speed after 25 hours.
(b) For each vehicle, if the speed is 200 mph after 10 hours, what was the
initial speed?
(c) For each option, if the initial speed is 30 mph, how long does it take
for the speed to be 100 mph?
2. You deposit 30 dollars in two different bank accounts.
Bank A: Every year the bank adds 5 dollars to your account.
Bank B: Every year the bank adds 5% of the previous year's balance.
(a) For each bank, determine the account balance after 25 years.
(b) For each bank, if the account balance is 200 dollars after 10 hours,
what was the initial deposit?
(c) For each bank, if the initial deposit is 30 dollars, how long does it take
for the account balance to be 100 dollars?
3. Two countries have the same population size today of 30 million people.
Country A: Every decade the population is increased by 5 million people.
Country B: Every decade the population is increased by 5%.
(a) For each country, determine the population size after 25 decades.
(b) For each country, if the population size is 200 million after 10 decades,
what was the current population?
(c) For each country, if the current population size is 30 million, how long
does it take for the population size to be 100 million?
4. For each of the two possibilities in each of three situations above,
determine
Vehicles: Speed after 30 minutes on the road.
Banks: Account balance after 6 months.
Countries: Population size after 5 years.