Question

In the year 2004, a company made $5.2 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 2007, to the nearest tenth of a million dollars?

Answer 1

Answer:

The company's profit in the year 2007 would be of $7.9 million.

Step-by-step explanation:

The profit of the company, in t years after 2004, is given by the following equation:

$P(t) = P(0)(1+r)^{t}$

In which P(0) is the profit in 2004, and r is the growth rate, as a decimal.

In the year 2004, a company made $5.2 million in profit.

This means that $P(0) = 5.2$

For each consecutive year after that, their profit increased by 15%.

This means that $r = 0.15$

Then

$P(t) = P(0)(1+r)^{t}$

$P(t) = 5.2(1+0.15)^{t}$

$P(t) = 5.2(1.15)^{t}$

How much would the company's profit be in the year 2007, to the nearest tenth of a million dollars?

2007 is 2007 - 2004 = 3 years after 2004. So this is P(3).

$P(t) = 5.2(1.15)^{t}$

$P(3) = 5.2(1.15)^{3} = 7.9$

The company's profit in the year 2007 would be of $7.9 million.