Math Problem Statement
In the year 2008, a company made $3.5 million in profit. For each consecutive year after that, their profit increased by 13%. How much would the company's profit be in the year 2010, to the nearest tenth of a million dollars?
Solution
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:
where:
- is the profit after years
- million (initial profit in 2008)
- (13% growth rate)
- is the number of years after 2008
Step 2: Find for the year 2010
Since 2010 is 2 years after 2008 (), we calculate:
Step 3: Round to the nearest tenth
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:
- What would the profit be in 2015 using the same formula?
- How long would it take for the profit to double?
- What is the total profit earned from 2008 to 2012?
- If the growth rate changed to 10% per year, how much would the profit be in 2012?
- What is the average annual profit from 2008 to 2015?
Tip: Exponential growth problems often require logarithms when solving for time!
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Math Problem Analysis
Mathematical Concepts
Exponential Growth
Percentage Increase
Algebra
Formulas
P_n = P_0 (1 + r)^n
Theorems
Exponential Growth Formula
Suitable Grade Level
Grades 9-12
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