Exponential Growth

A bank account earning continuously compounded interest doubles in value in 7.0 years. At the same interest rate, how long would it take to triple in value?

• 4.4 years

• 9.8 years

• 10.5 years

• 11.1 years

A sample of Ce-143 loses 99%of its radioactive matter in 199 hours. What is its half-life?

• 4 hours

• 6 hours

• 30 hours

• 100 hours

In which of the following models is dy/dt directly proportional to y?

I. y = e^(kt)+c

II. y = Ce^(kt)

III. y = 28^(kt)

• I and II only

• I and III only

• II and III only

• I, II, and III

An apple pie comes out of the oven at 425 degrees Fahrenheit. It is placed on the counter in a room that is 68 degrees Fahrenheit to cool. In 30 minutes it cooled to 195 degrees Fahrenheit. According to Newton's Law of Cooling, how many more minutes will pass before it is 100 degrees?

• 30 minutes

• 40 minutes

• 50 minutes

• 60 minutes

A colony of bacteria is grown under ideal conditions in a laboratory so the population increases with time. At the end of 3 hours there are 10,000 bacteria. At the end of 5 hours there are 40,000 bacteria. How many bacteria were initially present?

• 1,050 bacteria

• 1,150 bacteria

• 1,250 bacteria

• 1,350 bacteria

How long will it take an investment compounded continually at 5.25% interest to double?

• 13.2 years

• 14.2 years

• 15.2 years

• 16.2 years

There are 50 rabbits in a colony initially. In 5 month there are 100. What is the constant of proportionality, k?

• .02ln2

• .2ln2

• 2ln2

• 20ln2

How long will it take for $2000 to double in value if it earns 8.25% interested compounded quarterly?

• 8.19 years

• 8.29 years

• 8.39 years

• 8.49 years