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Question

1.) The cells of a certain culture of bacteria triple every 2 minutes. If there are 40 cells in the beginning, in how many minutes will there be more than 9500 cells?

  A.) 10 min

  B.) 4 min

  C.) 5 min

  D.) 11 min

2.)

A.) 4.5

B.) 1.5

C.) 3.5

D.) 2.5

 

Answer 1

1. 
   

Anytime you see phrases like "doubles" or "triples" every X period of time, start thinking in your head that this is framed as an exponential growth problem. A formula for exponential growth that might look familiar to you is:

f(t) = a * r^{t / p}

Where f(t) is the "number of things" after a certain amount of time, hence the notation f(t). a is the initial amount, as in the number of things at the beginning, when time t = 0. r is the rate of growth. t as we mentioned earlier is time. And finally p is the growth period. Challenge yourself before moving on to see how the phrases "triples every 2 minutes" and "40 cells in the beginning" would fit in the above equation.

After you've figured out what all the numbers in the question mean, remember that the question is asking you for a number of minutes given a number of bacteria. The formula above is the opposite in that it is providing a number of bacteria given a number of minutes. Rearrange the formula above so that the time t is isolated on one side and viola you've got a new formula that can help you answer your question.

2.

The same principle as the first question applies in the second question too. You are given a formula that provides the loudness L given an intensity I. But the final answer the question is looking for is for you to compare intensities not loudness, so the given formula won't work. If you can rearrange the given formula to isolate the intensity I on its own side of the equation, you'll be able to find out what the intensity I is given a loudness L. After that all that's left is to compare the intensity of a 97 decibel sound to the intensity of a 93 decibel sound. Remember that decibels measures loudness, so we will be able to figure out how intense a 97 or 93 decibel sound is given our new formula.