Question

Smith and Taylor work for the same company which pays them at the end of every month. They sign the following contracts for 24 months starting in January 2020 and finishing in December 2021:Smith: Paid $1100 in January 2020, increasing by $60 every month. Taylor: Paid $420 in January 2020, increasing by 14% month. every(a) Find Taylor's monthly salary in March 2021, rounded to the nearest dollar.(b) Find the total amount Smith receives in the first year of his contract, rounded to thenearest dollar.(c) Find the month and year in which total amount Taylor has received in his contract first exceeds the total amount Smith has received in his contract.

Answer 1

a. Taylor's monthly salary is $420 and increases by 14% per month. Hence, Taylor's monthly salary can be modeled by the exponential function written below:

`t(x)=420(1.14)^x`

where x = the number of months since January 2020.

So, counting the months from January 2020 to March 2021, 14 months have passed. Hence, we will replace "x" with 14.

`t(14)=420(1.14)^(14)`

Then, solve.

`t(14)=420(6.261349)`
`t(14)=2,629.7666\approx2,630`

Therefore, Taylor's monthly salary in March 2021 is approximately $2, 630.

b. Smith's monthly salary is $1,100 and increases by $60 per month. Since the amount of increase is a fixed amount, we can model Smith's salary using a linear function.

`s(x)=1,100+60x`

where "x" represents the number of months since January 2020.

Since we want to know the amount Smith receives in the first year of his contract, we will assume x = 12 since there are 12 months in a year.

`s(12)=1,100+60(12)`

Then, solve.

`s(12)=1,100+720`
`s(12)=1,820`

Hence, in the 1st year of his contract, Smith receives $1, 820.

c. Since want to know the month when Taylor's salary exceeds Smith's salary, let's calculate and compare their salary each month. See the comparison below.

As we can see in the table above, it is in December 2020 when Taylor's monthly salary exceeds the monthly salary of Smith.