Chapter 5 Exponential, Power, and Logarithmic Functions

1. Chapter 5Exponential, Power, and Logarithmic Functions Matthew Mador Timmy Ma Drake Freiberg Chris Ersevim

2. What is an exponential function? An exponential function is a continuous function with a variable in the exponent, and it is used to model growth or decay.

3. What is an logarithmic function? A logarithmic function is an exponent-producing function.

4. Chemistry You use logarithms when calculating the pH of a solution. For instance, if you know the concentration of the ions, you can find the pH by using the negative log base 10. For example, if the concentration of hydrogen ions in a solution is 5.0 x 10-4M… pH = -log [H+] = -log (5.0 x 10-4) = - (-3.30) = 3.30

5. Population Growth In the year 2000, there were 10 times more people on Earth than there were 300 years before. How did the population grow so fast? With population growth, new members of the population produce other new members. The population increases exponentially as time passes.

6. Richter Magnitude Scale The Richter Scale, which used to tell the magnitude of an earthquake, is a base-10 logarithmic scale. That’s why an earthquake with a magnitude 7.2 is ten times bigger than one with a magnitude of 6.2.

8. Compound Interest One of the most common examples of exponential growth is compound interest. Suppose you have $100 that you could put into either : • a checking account that earns no interest, • a savings account that earns 3 % compounded annually, • a savings account that earns 5% compounded annually, or • a certificate of deposit that earns 7% compounded annually. How would your results compare after 10 or 20 years?

9. Assuming you make no withdrawals, the money in the checking account will remain constant at $100. The money in the accounts that receive interest will obviously increase, but by how much? The longer your money remains in the account, the more dramatic the results.