Questions: f(t)=-23.27 t+200.17 thousand dollars gives the profit of a failing department store between 2011 and 2020, where t is the number of years since the end of 2011. a. What was the profit of the store at the end of 2008? (Round your answer to 2 decimal places.) thousand

f(t)=-23.27 t+200.17 thousand dollars gives the profit of a failing department store between 2011 and 2020, where t is the number of years since the end of 2011. a. What was the profit of the store at the end of 2008? (Round your answer to 2 decimal places.) thousand

Transcript text: f(t)=-23.27 t+200.17 thousand dollars gives the profit of a failing department store between 2011 and 2020 , where $t$ is the number of years since the end of 2011 . a. What was the profit of the store at the end of 2008? (Round your answer to 2 decimal places.) $\$$ $\square$ thousand

Solution

Solution Steps

To find the profit of the store at the end of 2008, we need to determine the value of $ t $ corresponding to the end of 2008. Since $ t $ is the number of years since the end of 2011, the end of 2008 is 3 years before the end of 2011. Therefore, $ t = -3 $. We will substitute $ t = -3 $ into the function $ f(t) $ to calculate the profit.

Step 1: Determine the Value of $ t $ for 2008

The function $ f(t) = -23.27t + 200.17 $ represents the profit in thousand dollars, where $ t $ is the number of years since the end of 2011. To find the profit at the end of 2008, we calculate $ t $ as follows: \[ t = 2008 - 2011 = -3 \]

Step 2: Substitute $ t = -3 $ into the Profit Function

Substitute $ t = -3 $ into the function $ f(t) $ to find the profit at the end of 2008: \[ f(-3) = -23.27(-3) + 200.17 \]

Step 3: Calculate the Profit

Calculate the value of $ f(-3) $: \[ f(-3) = 69.81 + 200.17 = 269.98 \]