To calculate the company's profit in the year 2010, we will use the concept of compound growth, where the profit increases by 13% each year after 2008.

Step 1: Set up the formula for compound growth.

The formula for compound growth is: $P = P_0 (1 + r)^t$ Where:

• $P_0$ is the initial profit (in 2008), which is $3.5 million.
• $r$ is the rate of growth per year, which is 13% or 0.13.
• $t$ is the number of years after 2008 (so for 2010, $t = 2$).
• $P$ is the profit in the year we are calculating.

Step 2: Plug in the values.

We need to find the profit in 2010, which is 2 years after 2008. So: $P = 3.5 \times (1 + 0.13)^2$ $P = 3.5 \times (1.13)^2$ $P = 3.5 \times 1.2769$ $P = 4.463 \text{ million dollars}$

Step 3: Round the answer.

To the nearest tenth of a million dollars, the profit in 2010 is approximately: $P \approx 4.5 \text{ million dollars}.$

So, the company's profit in 2010 is $4.5 million.

Would you like more details or have any further questions? Here are 5 related questions you might find interesting:

1. How would the profit look in 2015, 7 years after 2008?
2. If the company had a 10% increase instead of 13%, how would that change the 2010 profit?
3. What would the company’s profit be in 2010 if the growth rate were compounded monthly?
4. How could this model be adjusted for a situation with varying annual growth rates?
5. What other types of growth models might be applicable in this scenario, besides compound growth?

Tip: Compound growth can make a large impact over time, so even small percentage increases can lead to significant gains over multiple years.