Assignment:
Q1. A retailer you spoke with in New York City's fashion district imports haute couture from European designers. One of the accommodations which must be considered when importing fashion from other countries is the difference in the size charts. A function that will convert dress sizes in the United States to those in Italy is
g(x) = 2(x+12).
- Find the dress sizes in Italy that correspond to sizes 6, 10, and 14 in the United States
- Find a formula for the inverse of the function.
- Use the inverse function to find the dress sizes in the United States that correspond to 36, 44, and 60 in Italy.
Q2. Last week's profits from a dry cleaners was $2000. Suppose the $2000 is invested at interest rate k, compounded continuously, and grows to $2983.65 in 5 years.
- What is the interest rate?
- Find the exponential growth function.
- What will the balance be after 10 years?
- When will the $2,000 double?
Provide complete and step by step solution for the question and show calculations and use formulas.