Question

The projected worth (in millions of dollars) of a large company is modeled by the equation w = 206(1.1)^t The variable t represents the number of years since 2000. What is the projected annual percent of growth, and what should the company be worth in 2011?A. 11%; $646.52 millionB. 10%; $534.31 millionC. 10%; $587.74 millionD. 11%; $226.60 million

Answer 1

SOLUTION

From the function

$w=206\mleft(1.1\mright)^t$

Since t represents the time, we will substitute the value for t to find the worth w.

2000 to 2011 is 11 years, so t = 11. Substituting this into the equation we have

$\begin{gathered} w=206\mleft(1.1\mright)^t \\ \\ w=206\mleft(1.1\mright)^{11} \\ \\ w=206\times2.8531 \\ \\ w=587.74 \end{gathered}$

So, the worth is $587.74 million

From the funtion, the 1.1 shows a percent increase by 0.1.

That is from 1 to 1.1 means 1.1 - 1.0 = 0.1

0.1 x 100 = 10%.

Therefore, the correct answer is option C.