Question

Nathalia just landed a great job as an engineer where she will make $90,000 a year. The company she will work for guarantees a 4% pay increase each year so employees' salaries keep up with inflation. At the end of the year Nathalia will have made $90,000.

Create an explicit function that represents Nathalia's salary.



Use your function to predict how much Nathalia's salary will be in 10 years, Round

to the nearest dollar

Answer 1

To predict Nathalia's salary in 10 years with a 4% annual pay increase, an exponential growth formula is used. After calculating the values, Nathalia's salary is determined to be $133,222 after rounding to the nearest dollar.

Step-by-step explanation:

To create an explicit function that represents Nathalia's salary with a 4% pay increase each year, we use an exponential growth formula:

S(n) = P × (1 + r)^n

Where:

• S(n) is the salary after n years,
• P is the initial salary, which is $90,000,
• r is the annual pay increase rate, which is 4% or 0.04,
• n is the number of years.

Substituting the given values into the formula, we get:

S(n) = $90,000 × (1 + 0.04)^n

To predict Nathalia's salary in 10 years, we substitute n with 10:

S(10) = $90,000 × (1 + 0.04)^{10}

Now, we calculate the amount:

S(10) = $90,000 × (1.04)^{10}

S(10) = $90,000 × 1.48024

S(10) = $133,221.60

After rounding to the nearest dollar, Nathalia's salary in 10 years will be $133,222.