A.4.15.3 U.S. Dollars and Mexican Pesos
An American traveler who is heading to Mexico exchanges some U.S. dollars for Mexican pesos. At the time of his travel, 1 dollar can be exchanged for 19.32 pesos. At the same time, a Mexican businesswoman who is in the United States is exchanging some Mexican pesos for U.S. dollars at the same exchange rate. 1. Find the amount of money in pesos that the American traveler would get if he exchanged: a. 100 dollars b. 500 dollars 2. Write an equation that gives the amount of money in pesos, p, as a function of the dollar amount, d, being exchanged. 3. Find the amount that the Mexican businesswoman would get if she exchanged: a. 1,000 pesos b. 5,000 pesos 4. Explain why it might be helpful to write the inverse of the function you wrote earlier. Then, write an equation that defines the inverse function.
- "The amount of money in cents, c, is a function of the amount in dollars, d. What equation can we write to represent this function?" (c=100d)
- "How can we find the inverse function?" (We can reverse the process and solve for d. To find the amount in cents, c, we multiply the dollar amount, d by 100. To find the inverse, we divide the amount in cents by 100.)
- "Why might it be helpful to find the inverse function, in this case?" (If we know an amount in cents, we can find the amount in dollars. It gives us the amount in dollars as a function of the amount in cents.)
- "Let's say d=7w represents a function that gives the number of days, d, in w weeks. A student says that the inverse function is w=7d because now the variables are switched. Do you agree? Why or why not?" (No. To find the number of days in w weeks, we multiply w by 7. So to find the number of weeks, w, in d days, we need to divide d by 7, not multiply d by 7.)
- "In general, how can you check if two functions are inverses?" (We can check if the process done to get the output of the original function gets reversed in the inverse function. If a is the input in the original function and it gives b for the output, we can see if putting b in the inverse function gives a for the output.)