I gave Alexa a short period of time to work on her Quadratic Formula Homework paper.
We then moved into graphing exponential functions of the form f(x)=b^x. We worked out a few examples using x values from -2 to 2 in a chart. Alexa was able to tell that when 0<b<1, we have exponential decay. When b>1, we have growth. And if b=1, then it is not an exponential function. It is a horizontal line at y=1.
I gave Alexa a summary sheet for compound interest. She had to fill in the blanks and tell for what each variable of the interest formula stands. She did well with this activity. I then gave her 2 questions that asked her to find the amount of money after a certain number of years in the account with compounded interest. She was able to answer these questions with some guidance. I had to assist her with figuring out how many times the interest is compounded per year.
I gave her time to work on her quadratic formula take-home activity. We talked a bit about the expectation for completing homework. I told her that I think she can do it!
Compound Interest and Graphing Exponential Functions
Lesson Outline
We used the equation for compound interest to solve a question regarding how much money should be deposited in various accounts if we wanted to earn $3000 in 3 years. Alexa took notes while I worked the exercise on the board. She discovered that it was best to put money into an account earning 4% interest, compounded annually, rather than into an account earning less interest but compounded more frequently.
We then transitioned into graphing exponential functions. We used graphs to discover why f(x)=b^x has to have b>0, but not equal to 1, in order to be an exponential function.
Alexa and I talked a bit about our holiday break. I gave her a syllabus and talked with her about expectations for the remainder of the school year. Along with daily participation, I would like for her to complete 5 homework assignments each quarter, as well as attempt 2 in-class, open book assessments, in order to earn an "A" each 9-weeks.
Her first homework assignment is a review of using the quadratic formula. I spent some class time going over examples with her. We then talked about Compound Interest. She shared that she went to a bank over the break to set up an account. We went through scenarios of investing various amounts of money at 5% interest, compounded annually. Alexa was able to see that putting money in an account that earns interest is a very good thing, and that investing in the stock market or mutual funds can be an even better thing! Tomorrow we will look at the actual formula for compound interest and see how to use it.
Writing Exponential Functions for given situations
Lesson Outline
I had Alexa work out of the book to answer 5 word problems. The problems explained situations where she had to determine the initial value, ratios, and percent of increase. Once she defined them, she filled the values into the equation.
We completed our example of the Honda driving off the lot and losing value immediately, as well as gradually depreciating each year. Alexa had to write an equation for the depreciation, given that it lost 9% of it's value after driving off the lot. She did a fairly good job of understanding the scenario.
I introduced the idea of decay and half-lives with the element radium. We looked at an example of radium decaying, and I explained that a half-life is the amount of time it takes for half of a substance to decay. For radium-226, it's half-life it 1600 years. Alexa and I explored questions about the appropriate domain for the situation.
