onsecutive Growth and Decay Factors Active TIME REMAINING 51:50 2 The price of crude oil, per barrel, in the year 2006 was estimated at $\$ 66.02$. There was a $9.5 \%$ increase in the year 2007 and a $38.83 \%$ increase in the year 2008 . Determine the approximate value for a barrel of crude oil in the year 2008. Round your answer to the nearest cent. a. $\$ 128.74$ c. $\$ 179.27$ b. $\$ 91.66$ d. $\$ 100.36$ Please select the best answer from the choices provided A $B$ C D Mark this and relum Save and Exit Nert Submit

Step 1 ：Given that the price of crude oil per barrel in the year 2006 was estimated at \$66.02.

Step 2 ：In 2007, there was a 9.5% increase in the price. We can calculate the price in 2007 using the formula for compound interest: \(A = P(1 + r/n)^{nt}\), where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (in decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years. In this case, the interest is compounded once per year (n=1), the initial amount of money is the price in 2006, and the interest rate for 2007 is 9.5%. So, the price in 2007 is \(66.02(1 + 0.095/1)^{1*1} = \$72.29\).

Step 3 ：In 2008, there was a 38.83% increase in the price. We can calculate the price in 2008 using the same formula for compound interest, but this time the initial amount of money is the price in 2007, and the interest rate for 2008 is 38.83%. So, the price in 2008 is \(72.29(1 + 0.3883/1)^{1*1} = \$100.36\).

Step 4 ：Final Answer: The approximate value for a barrel of crude oil in the year 2008 is \(\boxed{\$100.36}\).