Problem Solving with Logs (Leaving Cert Mathematics): Quizzes

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Problem Solving with Logs
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What is the general form of the exponential growth equation given in the note?

y=Aebty = Ae^{bt}

In the equation y=Aebty = Ae^{bt}, what does the variable tt represent?

Time in hours

What is the value of tt at the start of the experiment?

t=0t = 0

What is the value of e0e^0?

11

Using initial conditions (100 bacteria at t=0t=0), what is the value of AA?

A=100A = 100

After finding A=100A = 100, what is the simplified equation?

y=100ebty = 100e^{bt}

What equation results from substituting 450 bacteria at 6 hours?

450=100e6b450 = 100e^{6b}

After dividing 450=100e6b450 = 100e^{6b} by 100, what is the result?

4.5=e6b4.5 = e^{6b}

What do we do to both sides of 4.5=e6b4.5 = e^{6b} to solve for bb?

Take natural log of both sides

What is the value of ln⁡(e)\ln(e)?

11

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