Question

Employees at a certain company are scheduled to earn a 1.9%1.9% pay increase each year to adjust for the cost of living. An employee starts at a salary of $35,000$35,000 per year and wants to know how long it will take to earn at least $40,000$40,000 per year. If the employee receives no additional raises, which statement is true?

Answer 1

Answer:

The time it will take to earn at least $40,000 per year is 7.

Step-by-step explanation:

The information provided explains that the salary of an employee has an exponential growth.

That is, an employees salary is increasing exponentially at a constant rate.

The exponential growth function is:

$y=a(1+r)^{n}$

Here,

y = final value

a = initial value

r = growth rate

n = time

Compute the time it takes for and employee's salary to increase from $35,000 to $40,000 as follows:

$40000=35000\times (1+0.019)^{n}$

$\frac{40000}{35000}=(1.019)^{n}$

$\frac{8}{7}=(1.019)^{n}$

Taking natural log on both sides,

$\ln(\frac{8}{7})=n\times \ln(1.019)$

$n=\frac{\ln (8/7)}{\ln (1.019)}$

$n=7.0945\\n\approx 7$

Thus, the time it will take to earn at least $40,000 per year is 7.

Answer 2

Answer:

D

Step-by-step explanation: