The company's profit follows an exponential growth pattern, given that it increases by 13% each year.

Step 1: Define the formula

The formula for exponential growth is:

$P_n = P_0 (1 + r)^n$

where:

• $P_n$ is the profit after $n$ years
• $P_0 = 3.5$ million (initial profit in 2008)
• $r = 0.13$ (13% growth rate)
• $n$ is the number of years after 2008

Step 2: Find $P_2$ for the year 2010

Since 2010 is 2 years after 2008 ($n = 2$), we calculate:

$P_2 = 3.5 (1.13)^2$

$P_2 = 3.5 \times 1.2769$

$P_2 \approx 4.4692$

Step 3: Round to the nearest tenth

$P_2 \approx 4.5$

Final Answer:

The company's profit in 2010 would be 4.5 million dollars.

Would you like a breakdown of a different approach or a verification of the calculation?

Here are five related questions you might find interesting:

1. What would the profit be in 2015 using the same formula?
2. How long would it take for the profit to double?
3. What is the total profit earned from 2008 to 2012?
4. If the growth rate changed to 10% per year, how much would the profit be in 2012?
5. What is the average annual profit from 2008 to 2015?

Tip: Exponential growth problems often require logarithms when solving for time!