An electrician's starting salary is $62,300 per year. Their salary increases by 6% each year. a) We need to write an equation to represent the electrician's salary, $S$, after $t$ years of work. b) We need to calculate the electrician's salary after 5 years.

1. Problem Description

An electrician's starting salary is $62,300 per year. Their salary increases by 6% each year.

a) We need to write an equation to represent the electrician's salary, $S$, after $t$ years of work.

b) We need to calculate the electrician's salary after 5 years.

2. Solution Steps

a) The salary increases by 6% each year, so the salary after $t$ years can be represented by an exponential growth formula. The initial salary is $62,

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0. The formula for exponential growth is:

$S = P(1 + r)^t$

Where:

$S$ = Salary after $t$ years

$P$ = Initial salary

$r$ = Rate of increase (as a decimal)

$t$ = Number of years

In this case, $P = 62300$ and $r = 0.06$.

So, the equation is:

$S = 62300(1 + 0.06)^t$

$S = 62300(1.06)^t$

b) To find the salary after 5 years, we need to plug in $t = 5$ into the equation we found in part (a):

$S = 62300(1.06)^5$

$S = 62300 * 1.3382255776$

$S = 83478.448083288$

Rounding to the nearest cent, the salary after 5 years is $83,478.

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3. Final Answer

a) $S = 62300(1.06)^t$

b) $83,478.45