Question: Describe the basic differences between linear growth and exponential growth.

Answer: Linear growth occurs when a quantity grows by the same absolute amount in each unit of​ time, and exponential growth occurs when a quantity grows by the same relative​ amount, that​ is, by the same​ percentage, in each unit of time.

Question: Money in a bank account earning compound interest at an annual percentage rate of​ 3% is an example of exponential growth.

Answer: The statement makes sense because the money in the account grows by the same​ percentage, which is an example of exponential growth

Question: A small town that grows exponentially can become a large city in just a few decades.

Answer: The statement makes sense because exponential growth leads to repeated​ doublings, making the population increase rapidly.

Question: Human population has been growing exponentially for a few​ centuries, and this trend can be expected to continue forever in the future.

Answer: The statement does not make sense because exponential growth cannot continue indefinitely.

Question: log 10 pi

Answer: log=between 0-1

pi= 1-10

Question: Given a​ half-life, explain how you calculate the value of an exponentially decaying quantity at any time t.

Answer: Let t be the amount of time that has passed and Upper T Subscript ha l fThalf be the​ half-life. The quantity after time t is the original quantity times this factor of left parenthesis one half right parenthesis Superscript t divided by Upper T Super Subscript ha l f

1

2t/Thalf

Question: Briefly describe exact doubling time and​ half-life formulas. Explain all their terms.

Answer: no negative; fractional growth decay

no log102; fractional decay

Question: compound interest formula

Answer: A = P(1 + r/n)^(n x t),

r is the rate,

n is the number of times compounded,

t is time

Question: What is the difference between simple interest and compound​ interest? Why do you end up with more money with compound​ interest?

Answer:

Question: Explain why the term​ APR/n appears in the compound interest formula for interest paid n times a year.

Answer: APR represents the annual percentage rate​ (as a​ decimal). To account for the interest paid n times a​ year, this annual​ (yearly) rate needs to be divided by the number of compounding periods per​ year, n.