Due to inflation, the dollar loses value according to $f(t)=(0.97)^{t}$, where $t$ is time in years since 2020 and $f(t)$ is the value of the future dollar in terms of today's money. In terms of today's money, what will the dollar be worth in 2048? Round to the nearest cent. 67 cents 80 cents 43 cents 105 cents Submit Question

Step 1 ：The problem is asking for the value of the dollar in 2048 in terms of today's money. This can be calculated by substituting \(t\) with the number of years from 2020 to 2048 in the given function \(f(t)=(0.97)^{t}\).

Step 2 ：Calculate the number of years from 2020 to 2048, which is \(t = 2048 - 2020 = 28\).

Step 3 ：Substitute \(t = 28\) into the function \(f(t)=(0.97)^{t}\) to get the value of the dollar in 2048 in terms of today's money. The value is \(f(28) = (0.97)^{28} = 0.42619520516862314\).

Step 4 ：Round the value to the nearest cent to get the final answer. The rounded value is \(0.43\).

Step 5 ：Final Answer: The dollar will be worth \(\boxed{43}\) cents in 2048 in terms of today's money.