Problem
DEIAILS TANAPCALC10 6.5.051. MY NOTES PRACTICE ANOTHER Cell Phone Ad Spending A certain industry's ad spending between $2005(t=1)$ and $2011(t=7)$ is projected to be \[ S(t)=0.89 t^{0.97} \quad(1 \leq t \leq 7) \] where $S(t)$ is measured in billions of dollars and $t$ is measured in years. What is the projected average spending per year on these ads between 2005 and 2011 ? (Round your answer to two decimal places.) \[ \$ \] billion/yr Need Help? Road it Submit Answer
Solution
Step 1 ：Define the function \(S(t) = 0.89 \cdot t^{0.97}\) where \(S(t)\) is measured in billions of dollars and \(t\) is measured in years.
Step 2 ：Calculate the total spending from 2005 to 2011 by integrating the function \(S(t)\) from \(t=1\) to \(t=7\).
Step 3 ：Calculate the average spending per year by dividing the total spending by the number of years, which is 7.
Step 4 ：The projected average spending per year on these ads between 2005 and 2011 is approximately \$2.92 billion per year.
Step 5 ：\(\boxed{2.92}\) billion dollars per year is the final answer.
