I gave Samantha the practice test on logarithms and exponential equations and she was able to finish it easily in less time than I expected. She was able to convert from exponential expressions to logarithmic expressions with little difficulty and was also able to do the reverse of the process. She also was able to change compact logarithmic expressions into expanded expressions and vice versa. The test also had some exponential equations to solve and some logarithmic expressions to evaluate. There was no assignment.

Today, Sam and I watched two videos about learning a language with a specific purpose(warm-up) . Sam wrote some examples related to the unit- textbook. Sam was able to apply vocabulary in real context. She used vocabulary words to build her own sentences.

I continued to work with Samantha on expanding and contracting logarithmic expressions, solving exponential equations, and evaluating logarithmic expressions for common and natural logarithms. We completed the textbook portion of her review. Next time, we will use my practice test for her final test on logarithms. There was no assignment.

We discussed and used video images to outline the results on the body of toxic chemicals which can be found in cosmetics. Aluminum products found in antiperspirants were singled out and the effect on skin and eventually on the system when absorbed was presented.
We discussed absorption of essential oils which are found in many products, and how the location of application will effect the absorption.

Define and discuss the difference between permeability (penetration) and absorption. Permeability represents the amount of a topically applied substance that exists between the top and the bottom layer of the epidermis. There is no absorption into the blood and cannot affect the body systems. Skin absorption occurs when the applied chemical reaches the dermal layer and absorbs into the blood stream. Briefly discussed how skin care ingredient penetration works. Small particle size products are permeable and can be uptaken by skin cells. After a period of time they will be secreted out of the skin cells and enter the blood. Large particles will move between the skin cells and enter the circulation. Non absorbed particles may be temporarily absorbed by some glands and absorbed over time.

Discussion of the importance of considering the "ecological diversity" of the skin when considering a product for topical use. Substances should be used carefully on the skin as many compounds may cause an allergic response or act as feeding grounds for some of the 1000 species of bacteria which inhabit the skin. The allergic response was outlined, including terms like antigen, allergen, antibodies, and histamine. The overgrowth of bacteria or yeast when topical cosmetics are used needs to be addressed when manufacturing these products. A list of 26 allergenic substances will be presented and briefly discussed.

Sam took the final exam for the entire period and was very gratified to have completed the required exam and coursework.

I worked with Samantha on problems requiring expansion and contraction of logarithmic expressions, solutions of logarithmic equations including natural logarithms, and evaluations of logarithmic expressions to numbers. We used both the chapter review and the chapter test to do selected problems. There was no assignment.

A dilation of a figure is when you change its shape by a dilation factor of k. The initial points can be defined as (x,y), and the dilated points are (kx, ky). There is always a center of dilation, which may or may not be the origin. If k>1, then the dilation results in a larger shape or longer distance of a point from the center of dilation. If k<1, then the shape shrinks, or the point gets closer to the center of dilation. Sam and I looked at cases where we were given the dilation factor and had to dilate the point or shape based on the factor. She then had to find the dilation factor when given a shape and its dilated image. She thought that these types of transformations were easier than rotations.

Using a educator video,the anatomy and physiology of the skin was reviewed, and new areas addressed. We reviewed the epidermal, dermal and subdermal layers. Each layer was discussed in regards to major structures, how they effect the health of the person and the effects of applying various materials to the skin will bring about.
Melanin, keratin, blood vessels, sweat glands, sebaceous glands and hair follicles were discussed, along with how these parts are affected by topical applications like makeups and foundations.