Problem 1: Bill invests $12,000 at 11.5% API while Jill invests $8,000 at 15% API. Assuming each investment is compound annually, at what year will each investment have equal value? Graph both functions to identify a solution.

Problem 2: A infectious bacterium reproduces (divides) every 4 hours (which works out to a growth rate r = 0.189 per hour). Assume no bacteria die/are destroyed during this infection. If your infection begins with 1200 bacteria:

• how many bacteria will exist in your body 12 hours later?
• Graph the bacteria growth vs time below.

Problem 3: You buy a new car for $35,000. If the car depreciates at a yearly rate of 25%, predict/calculate:

• the car's value in 5 years.
• the car's value in 10 years
• Fill in the t chart and graph the vehicle's depreciation.

ANSWERs:

value after 5 yrs = __________

value after 10 yrs = _________

Problem 4: You have two investments A and B. At t = 0 years:

• Investment A is $10,000 which is growing at an API = 5.6% (compounded once per year).

• Investment B is $100,000 which is decaying (losing value) at an API = 10.2% (compounded once per year).

When will both investments be at the same value? Show both curves on the Cartesian and Semi-log graphs.