Question

when ashley was hired as a nurse at blue ridge hospital, her starting salary was $54,000. ashleys contract states that her salary will increase by the same percentage each year. after working there for one year, ashleys salary rose to $55,080. write an exponential equation in the form $y = a(b)^x$ that can model ashley’s salary, $y$, $x$ years after she started working there. use whole numbers, decimals, or simplified fractions for the values of $a$ and $b$. $y = square$ how much can ashley expect her salary to be 5 years after she started working at blue ridge hospital? round to the nearest whole number. $\\$ square$

Explanation:

Step1: Identify initial value $a$

The starting salary is the initial value, so $a = 54000$.

Step2: Calculate growth factor $b$

Divide year 1 salary by initial salary:
$b = \frac{55080}{54000} = 1.02$

Step3: Write exponential equation

Substitute $a$ and $b$ into $y=a(b)^x$:
$y = 54000(1.02)^x$

Step4: Compute salary at 5 years

Substitute $x=5$ into the equation:
$y = 54000(1.02)^5$
First calculate $(1.02)^5 \approx 1.1040808032$
Then compute $54000 \times 1.1040808032 \approx 59620.36$

Step5: Round to nearest whole number

Round $59620.36$ to the nearest integer: $59620$

Answer:

$y = 54000(1.02)^x$
$\$59620$