James has worked for the same company his entire life.His current income is $100,000 per year.When he was originally hired,he made $50,000 per year.The company has given James a consistent raise of 2% every year.How long has James been with the company?

Question

Quizplus · Accepted Answer

Let x represent the number of years James has been with the company.

From the problem, we know that:

- When James was originally hired, he made $50,000 per year. 
- James currently makes $100,000 per year. 
- James has received a consistent raise of 2% every year.

Using this information, we can set up the following equation:

$50,000(1.02)^x = $100,000

Simplifying this equation, we get:

(1.02)^x = 2

To solve for x, we can take the logarithm of both sides:

log(1.02)^x = log2

Using the power rule of logarithms, we can move the exponent down:

x · log(1.02) = log2

Dividing both sides by log(1.02), we get:

x = log2 / log(1.02)

Using a calculator, we find that x = 34.65.

Since we're dealing with whole years, we can round up to the nearest year and conclude that James has been with the company for 35 years (Choice C).

James Has Worked for the Same Company His Entire Life