Question

1. Your starting salary at a new company is $34,000 and it increases by 2.5% each year. a) Write a function for this situation in terms of t for time: b) What will your salary be in 5 years? Round your answer to the nearest dollar. c) What will your salary be in 10 years? Round your answer to the nearest dollar. d) What will your salary be when you reach retirement (30 years)? Round your answer to the nearest dollar. e) How many years does it take to earn a salary of $100,000? Round your answer to the nearest year.

Answer 1

Given :

Starting salary at a new company is $34,000 and increases by 2.5% each year.

Solution :

(a)Function for this situation =  $34,000(1+\frac{2.5}{100})^t$

(b) Salary in 5 years =

$34000(1+\frac{2.5}{100})^5$

= 34000(1.025)⁵

= 34,000 × 1.13140821

= 38,467.8792 ≈ $38,468

Your salary will be $38,468 in 5 years

(c) Salary will be in 10 years =

$34,000(1+\frac{2.5}{100})^{10}$

= 34,000(1.025)¹⁰

= 34,000 × 1.28008454

= 43,522.8745 ≈ $43,523

Your salary will be $43,523 in 10 years.

(d) Salary will be in 30 years =

$34,000(1+\frac{2.5}{100})^{30}$

= 34,000(1.025)³⁰

= 34,000 × 2.09756758

= 71,317.2977 ≈ $71,317

Your salary will be $71,317, when you reach retirement.

(e) $34000(1+\frac{2.5}{100})^t=100,000$

Solve for t

$34000(1.025)^t=100,000$    [divide 34,000 both side]

$1.025^t=\frac{50}{17}$       [take log both side]

t = 43.689 ≈ 44 years

It will take 44 years to earn a salary of $100,000.