Question

In the year 2000, a company made $4.7 million in profit. For each consecutive year after that, their profit increased by 15%. How much would the company's profit be in the year 2004, to the nearest tenth of a million dollars?

Answer 1

Answer: $8.2 million.

Explanation:

If we have a quantity A, and we have an increase of x%, this can be written as:

A + (x%/100%)*A

Now, for this particular case we have:

In year 2000 (we can define this year as the year zero, y = 0) the initial value is $4.7 million.

The next year, y = 1, there is an increase of 15%, then we will have a profit of:

P = $4.7 million + (15%/100%)*$4.7 million = $4.7 million +  0.15*$4.7 million

P = $4.7 million*(1 + 0.15) = $4.7 million*(1.15)

in the next year, y = 2, the profit will be:

P =  $4.7 million*(1.15) + (15%/100%)* $4.7 million*(1.15)

  = $4.7 million*(1.15) + 0.15* $4.7 million*(1.15)

   = $4.7 million*(1.15)^2

We already can see the pattern, the profit in the year y will be:

P(y) = $4.7 million*(1.15)^y

In particular, in the year 2004 we have y = 4, then the profit that year will be:

P(4) = $4.7 million*(1.15)^4 = $8.2 million.