UCSS Math III 4A.2.5 Example 1
- Walch Education
The number of electric vehicles () sold in the United States within 3 years of their introduction to the market can be modeled by the logarithmic function , where is the number of vehicles sold in thousands and is the number of years after introduction to the market. The number of hybrid vehicles () sold within 3 years of their introduction to the market can be modeled by the logarithmic function . At what value of was an equal number of each vehicle sold, and which type of vehicle had greater sales over the 3 introductory years? Explain your reasoning with references to the terms in the function and how they compare.
- Set .
- Solve the resulting equation for .
- Rewrite the resulting equation using an inverse function.
- Interpret the resulting value of in terms of the conditions of the original problem.
- Check the value of found in step 3 by substituting it back into the functions and .
- Show which vehicle type had greater sales over the 3-year period by comparing the characteristics of each function.