We looked at examples of exponential growth with the bunny population in Central Park. Alexa was asked to think of a reasonable domain and a function for the situation. I then introduced to her the scenario of a new car depreciating after being driven off the lot, as well as the usual depreciation that occurs over time.

Today we looked at our examples of the exponential growth of a bond fund, and the exponential decay of the fish population in Lake Placid. Using the formulas, we found the amounts after 10 and 20 years. Alexa learned how to sketch the graphs of exponential growth and decay, using our table of values.

We continued our discussion of exponential growth and decay today. Alexa was able to write equations to represent them. F(x) = ab^x, where a is the initial amount, b is the amount of growth or decay, and x is amount of time. In cases of exponential growth, the variable b is equal to 1 + (Rate of increase). In cases of exponential decay, the variable b is equal to 1 - (rate of decrease).

Alexa completed her rational equations, and answered the questions correctly. I introduced Exponential Functions to her. A linear function has a constant rate of change and is a straight line. A quadratic function has a variable raised to the second power, and its graph is a parabola. An exponential function increases exponentially, and either shows growth or decay. I showed Alexa a chart of different functions, and she was able to see that the exponential functions start off increasing slowly, but then start to rapidly increase. An asymptote of the graph is the line that the graph gets closer and closer to but never touches or crosses.

Alexa was absent today

We celebrated Alexa's acceptance to Lynn University. She was in a social mood, and was chatty with two of her other female schoolmates. During our afternoon session, she observed the school-wide holiday activity celebration.

Alexa did an excellent job working through more exercises on solving rational equations. She encountered a problem that required her to factor out a negative 1. She recognized that the negative needed to come out. I had to explain to her that it affected the sign of the numerator. Otherwise, she did a great job.

Today Alexa stood at the board and solved rational equations. It was amazing to see her work out the problems and talk through the process out loud. I think that it helped her learning and confidence!

Alexa worked on exercises 6-11, solving rational equations. She did well with them. We are almost finished with this unit.

I taught Alexa how to solve rational equations by finding the common denominator of the rational expressions, then multiplying both sides of the equation by the common denominator. It is important that we multiply every term by the common denominator. This will sometimes result in a quadratic equation, which will then have to be factored before it can be solved.