An economist predicts that the buying power \( \mathrm{B}(\mathrm{x}) \) of a dollar x years from now will decrease according to the formula \( \mathrm{B}(\mathrm{x})=0.95^{\mathrm{x}} \). How much will today's dollar be worth in 4 years? Round the answer to the nearest cent. A. \( \$ 3.80 \) B. \( \$ 0.81 \) C. \( \$ 0.98 \) D. \( \$ 3.73 \)

To find the value of today's dollar in 4 years, we can simply plug \( x = 4 \) into the formula: \[ B(4) = 0.95^{4} \approx 0.8145 \] This means today's dollar will be worth approximately \( 0.8145 \). When rounded to the nearest cent, that would be: \[ \text{Value in 4 years} \approx \$ 0.81 \] Therefore, the correct answer is: B. \( \$ 0.81 \) --- Did you know that the concept of "buying power" directly relates to inflation? The decline in purchasing power means that over time, you can buy less with the same amount of money. Economists gauge inflation rates through various indicators, allowing consumers and businesses to make informed financial decisions! In practical terms, understanding this concept can help you plan for future expenses and savings. For instance, investing your money into assets that appreciate over time can counteract the loss of value due to inflation. So, next time you're considering a purchase, think about how inflation might impact that dollar in the future!