Question

The projected worth (in millions of dollars) of a large company is modeled by the equation w= 241(1.03)^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 2012?A. 3%; $343.61 millionB. 3%; $333.60 millionC. 13%; $248.23 millionD. 13%; $353.92 million

Answer 1

The projected worth of a large company is modeled by:

`w=241(1.03)^t`

The general formula for an exponential function is:

`\text{Present }=\text{past}(1+growth-rate)^t\text{ }`

Comparing the general formula with the projected worth of the large company

`w=241(1+0.03)^t`

Hence, the annual percent growth would be:

`0.03*100\text{\%}=3\text{\%}`

The worth of the company in 2012 would be:

`\begin{gathered} w=241(1.03)^t \\ t=2012-2000=12 \\ \text{put }t=12 \\ w=241(1.03)^(12) \\ w=343.61 \end{gathered}`

Therefore, the projected annual percent of growth and the worth of the company in 2012 would be:

`3\text{\%; \$343.61 million \lbrack{}option A\rbrack}`