De shawn is in his fifth year of employment as a patrol officer for the metro police. his salary for his first year of employment was $47,000. each year after the first, his salary increased by 4% of his salary the previous year.

to obtain the sum of deshawn's salaries for the first five years of service, we can use f(x)=47,000(1.04)^x , where x gives the salary x years after his first year.

salary after 5 years = f(0) + f(1) + f(2) + f(3) + f(4) +f(5) = $245,567.

if deshawn continues his employment at the same rate of increase in yearly salary, for which year will the sum of his salaries first exceed $1,000,000?

(the answer should be 16, but i don't know how to get it.)

After 16 years De Shawn salary will exceed $1000000.

Step-by-step explanation:

First year salary of De Shawn as a petrol officer was $47000.

Each year increase in his salary was 4%.

Second year his salary will be = ($47000 + 4% of $47000) = $48880

Third year the salary will be = ($48880 + 4% of 48880) = $50835.20

Then every year his salary will be $47000, $48880, $50835...........

The sequence formed will be a geometric sequence having common ratio 'r' = (1+0.04) = 1.04

First term of this sequence = $47000

Since sum of a geometric sequence is represented by

We have to find the value of x (Number of years) after which the salary will be = $1000000

21.2766×0.04 + 1 =

1.851 =

By taking log on both the sides

log(1.851) =

0.2764 = xlog(1.04)

x =

x = 16.26 years

Therefore, after 16 year De Shawn's salary will exceed $1000000.

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation:

a reflection across the x axis and a 90 degree rotation left and right.