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: $t = 2008 - 2011 = -3$